{"id":1341,"date":"2026-03-06T12:16:20","date_gmt":"2026-03-06T10:16:20","guid":{"rendered":"https:\/\/blog.edu.turku.fi\/allu\/?page_id=1341"},"modified":"2026-03-25T08:57:27","modified_gmt":"2026-03-25T06:57:27","slug":"kongruenssi","status":"publish","type":"page","link":"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/lukuteoria\/kongruenssi\/","title":{"rendered":"Kongruenssi"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" href=\"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/lukuteoria\/\" style=\"background-color:#d6d6ff\">Palaa takaisin<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Kongruenssi<\/h2>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-1&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-1-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-1\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Teoria<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-1\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-1-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Kongruenssi-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Tiedoston Kongruenssi upotus.\"><\/object><a id=\"wp-block-file--media-35a87bcf-bce7-4424-8226-c99bbb15bc91\" href=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Kongruenssi-1.pdf\">Kongruenssi<\/a><a href=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Kongruenssi-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-35a87bcf-bce7-4424-8226-c99bbb15bc91\">Lataa<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoihin, perus ja vaikeisiin teht\u00e4viin.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#e6f3b7\">Helppo<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color has-text-align-center wp-element-button\" style=\"background-color:#d6d6ff\">Perus<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#fcd8c8\">Vaikea<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 1.<\/strong> Tutustutaan kongruenssiin.<\/h2>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-13\" class=\"h5p-iframe\" data-content-id=\"13\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Kongruenssi\"><\/iframe><\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-3&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-3-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-3\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Kysymykset kirjallisina<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-3\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-3-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<ol start=\"1\" class=\"wp-block-list\">\n<li>Mit\u00e4 kongruenssi kuvaa matematiikan lukuteoriassa?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a. Kahdella luvulla on sama kokonaisosa&nbsp;<\/li>\n\n\n\n<li>b. Kahdella luvulla on sama jakoj\u00e4\u00e4nn\u00f6s&nbsp;<\/li>\n\n\n\n<li>c. Kahdella luvulla on sama kerroin&nbsp;<\/li>\n\n\n\n<li>d. Kaksi kuviota&nbsp;ovat&nbsp;samanlaisia&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>Ovatko symmetriset kuviot kongruentteja?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. Ei&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li>Mill\u00e4&nbsp;modulon&nbsp;arvolla viikonp\u00e4iv\u00e4t ovat kongruentteja?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a. 8&nbsp;<\/li>\n\n\n\n<li>b. 7&nbsp;<\/li>\n\n\n\n<li>c. 6&nbsp;<\/li>\n\n\n\n<li>d. 30&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li>Perustuuko RSA-salaus kongruenssiin?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. Ei&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol start=\"5\" class=\"wp-block-list\">\n<li>Onko kuukausien kierto kongruentti&nbsp;modulo&nbsp;11 kanssa?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. Ei&nbsp;&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol start=\"6\" class=\"wp-block-list\">\n<li>Mill\u00e4&nbsp;modulon&nbsp;arvolla kuukausien kierto on kongruentti?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a. 12&nbsp;<\/li>\n\n\n\n<li>b. 30&nbsp;<\/li>\n\n\n\n<li>c. 31&nbsp;<\/li>\n\n\n\n<li>d. 24&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol start=\"7\" class=\"wp-block-list\">\n<li>Onko pelilaudalla kiert\u00e4minen kongruentti?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. Ei&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol start=\"8\" class=\"wp-block-list\">\n<li>Onko liikennevalojen toiminta kongruenttia?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. Ei&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol start=\"9\" class=\"wp-block-list\">\n<li>Onko p\u00e4ivien kierto kongruenttia lyhyell\u00e4 aika v\u00e4lill\u00e4?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. Ei<strong>&nbsp;<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol start=\"10\" class=\"wp-block-list\">\n<li>Onko p\u00e4ivien kierto kongruenttia pitk\u00e4ll\u00e4 aika v\u00e4lill\u00e4 noin&nbsp;400-600&nbsp;vuotta?&nbsp;\n<ul class=\"wp-block-list\">\n<li>a.<strong> <\/strong>Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. Ei&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-2&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-2-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-2\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-2\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-2-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<ol class=\"wp-block-list\">\n<li>b. Kahdella luvulla on sama jakoj\u00e4\u00e4nn\u00f6s<\/li>\n\n\n\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. 7&nbsp;<\/li>\n\n\n\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. Ei&nbsp;&nbsp;<\/li>\n\n\n\n<li>a. 12&nbsp;<\/li>\n\n\n\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>a. Kyll\u00e4&nbsp;<\/li>\n\n\n\n<li>b. Ei&nbsp;&nbsp;<\/li>\n\n\n\n<li>a. Kyll\u00e4&nbsp;<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 2.<\/strong> Tutki, ovatko annetut lausekkeet totta vai eiv\u00e4t. Perustele vastaus.<\/h2>\n\n\n\n<p><strong>a)<\/strong> <math data-latex=\"51\\equiv16\\ \\left(mod\\ 5\\right)\"><semantics><mrow><mn>51<\/mn><mo>\u2261<\/mo><mn>16<\/mn><mtext>&nbsp;<\/mtext><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mi>m<\/mi><mi>o<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mn>5<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">51\\equiv16\\ \\left(mod\\ 5\\right)<\/annotation><\/semantics><\/math><br><strong>b) <\/strong><math data-latex=\"22\\equiv13\\ \\left(mod\\ 3\\right)\"><semantics><mrow><mn>22<\/mn><mo>\u2261<\/mo><mn>13<\/mn><mtext>&nbsp;<\/mtext><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mi>m<\/mi><mi>o<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mn>3<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">22\\equiv13\\ \\left(mod\\ 3\\right)<\/annotation><\/semantics><\/math><br><strong>c)<\/strong> <math data-latex=\"36\\equiv19\\ \\left(mod\\ 8\\right)\"><semantics><mrow><mn>36<\/mn><mo>\u2261<\/mo><mn>19<\/mn><mtext>&nbsp;<\/mtext><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mi>m<\/mi><mi>o<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mn>8<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">36\\equiv19\\ \\left(mod\\ 8\\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-4&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-4-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-4\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-4\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-4-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a) Tosi, koska lukujen 51 ja 16 erotus on jaollinen luvulla 5.<br> <math data-latex=\"\\frac{51-16}{5}=\\frac{35}{5}=7\"><semantics><mrow><mfrac><mrow><mn>51<\/mn><mo>\u2212<\/mo><mn>16<\/mn><\/mrow><mn>5<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>35<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{51-16}{5}=\\frac{35}{5}=7<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>b) Tosi, koska lukujen 22 ja 13 erotus on jaollinen luvulla 3.<br> <math data-latex=\"\\frac{22-13}{3}=\\frac{9}{3}=3\"><semantics><mrow><mfrac><mrow><mn>22<\/mn><mo>\u2212<\/mo><mn>13<\/mn><\/mrow><mn>3<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>9<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{22-13}{3}=\\frac{9}{3}=3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>c) Ep\u00e4tosi, koska lukujen 36 ja 19 erotus ei ole jaollinen luvulla 8.<br> <math data-latex=\"\\frac{36-19}{8}=\\frac{17}{8}=2\\frac{1}{8}=2{,}125\"><semantics><mrow><mfrac><mrow><mn>36<\/mn><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><mn>8<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>17<\/mn><mn>8<\/mn><\/mfrac><mo>=<\/mo><mn>2<\/mn><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><mo>=<\/mo><mn>2,125<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{36-19}{8}=\\frac{17}{8}=2\\frac{1}{8}=2{,}125<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 3. <\/strong>Kirjoita teht\u00e4v\u00e4nantoa vastaava kongruenssi.<\/h2>\n\n\n\n<p><strong>a)<\/strong> Jakolasku <math data-latex=\"\\frac{71}{6}\"><semantics><mfrac><mn>71<\/mn><mn>6<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{71}{6}<\/annotation><\/semantics><\/math> jakoj\u00e4\u00e4nn\u00f6s on 5.<br><strong>b) <\/strong>Olet pelilaudalla ruudussa 29 ja siirryt 18 ruutua eteenp\u00e4in. Yksi pelilaudan kierros on 40 ruutua.<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-5&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-5-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-5\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-5\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-5-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a) <math data-latex=\"71\\equiv5\\left(mod\\ 6\\right)\"><semantics><mrow><mn>71<\/mn><mo>\u2261<\/mo><mn>5<\/mn><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mi>m<\/mi><mi>o<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mn>6<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">71\\equiv5\\left(mod\\ 6\\right)<\/annotation><\/semantics><\/math><br>b) <math data-latex=\"47\\equiv7\\left(mod\\ 40\\right)\"><semantics><mrow><mn>47<\/mn><mo>\u2261<\/mo><mn>7<\/mn><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mi>m<\/mi><mi>o<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mn>40<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">47\\equiv7\\left(mod\\ 40\\right)<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 4.<\/strong> Ratkaise sanalliset teht\u00e4v\u00e4t.<\/h2>\n\n\n\n<p><strong>a) <\/strong>Juho ja Elli juoksevat 400m rataa ymp\u00e4ri. Elli on juossut 350m ja Juho 2150m. Ovatko Elli ja Juho samassa kohdassa juoksurataa?<br><strong>b) <\/strong>T\u00e4n\u00e4\u00e4n on keskiviikko, mik\u00e4 viikonp\u00e4iv\u00e4 on 74 p\u00e4iv\u00e4n p\u00e4\u00e4st\u00e4?<br><strong>c)<\/strong> Onko kello saman verran\u00a06\u00a0tunnin ja\u00a054\u00a0tunnin p\u00e4\u00e4st\u00e4?\u00a0<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-6&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-6-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-6\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-6\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-6-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a) <strong>Eiv\u00e4t ole<\/strong> samassa kohdassa sill\u00e4 kongruenssi\u00a0<math data-latex=\"350\\equiv2150\\left(mod\\ 400\\right)\"><semantics><mrow><mn>350<\/mn><mo>\u2261<\/mo><mn>2150<\/mn><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mi>m<\/mi><mi>o<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mn>400<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">350\\equiv2150\\left(mod\\ 400\\right)<\/annotation><\/semantics><\/math> ei pid\u00e4 paikkaansa, koska<br> <math data-latex=\"\\frac{2150-350}{400}=\\frac{1800}{400}=4\\frac{1}{2}\"><semantics><mrow><mfrac><mrow><mn>2150<\/mn><mo>\u2212<\/mo><mn>350<\/mn><\/mrow><mn>400<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1800<\/mn><mn>400<\/mn><\/mfrac><mo>=<\/mo><mn>4<\/mn><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2150-350}{400}=\\frac{1800}{400}=4\\frac{1}{2}<\/annotation><\/semantics><\/math>\u00a0\u00a0<\/p>\n\n\n\n<p>b) 74 p\u00e4iv\u00e4n p\u00e4\u00e4st\u00e4 on<strong>torstai<\/strong>, koska <math data-latex=\"\\frac{74-3}{7}=\\frac{71}{7}=10\\ \\frac{1}{7}\"><semantics><mrow><mfrac><mrow><mn>74<\/mn><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><mn>7<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>71<\/mn><mn>7<\/mn><\/mfrac><mo>=<\/mo><mn>10<\/mn><mtext>&nbsp;<\/mtext><mfrac><mn>1<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{74-3}{7}=\\frac{71}{7}=10\\ \\frac{1}{7}<\/annotation><\/semantics><\/math>. Joten jakoj\u00e4\u00e4nn\u00f6s on 1 eli keskiviikkoon pit\u00e4\u00e4 lis\u00e4t\u00e4 yksi p\u00e4iv\u00e4.<\/p>\n\n\n\n<p>c) <strong>Kyll\u00e4<\/strong> on, koska lukujen erotus on jaollinen 24 tunnilla.\u00a0<br><math data-latex=\"\\frac{54-6}{24}=\\frac{48}{24}=2\"><semantics><mrow><mfrac><mrow><mn>54<\/mn><mo>\u2212<\/mo><mn>6<\/mn><\/mrow><mn>24<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>48<\/mn><mn>24<\/mn><\/mfrac><mo>=<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{54-6}{24}=\\frac{48}{24}=2<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 5.<\/strong> Etsi pienin mahdollinen luonnollinen luku<\/h2>\n\n\n\n<p><strong>a)<\/strong> Joka on kongruentti luvun 29 kanssa modulo 12.<br><strong>b)<\/strong> Joka on kongruentti luvun 451 kanssa modulo 7.<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-7&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-7-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-7\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-7\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-7-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a) <math data-latex=\"\\frac{29}{12}\\approx2,41667\"><semantics><mrow><mfrac><mn>29<\/mn><mn>12<\/mn><\/mfrac><mo>\u2248<\/mo><mn>2,41667<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{29}{12}\\approx2,41667<\/annotation><\/semantics><\/math>, joten kokonaisosa on 2<br> <math data-latex=\"29-12\\cdot2=5\"><semantics><mrow><mn>29<\/mn><mo>\u2212<\/mo><mn>12<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>=<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">29-12\\cdot2=5<\/annotation><\/semantics><\/math><br>vastaus: <strong>5<\/strong><\/p>\n\n\n\n<p>b) <math data-latex=\"\\frac{347}{4}\\approx86,75\"><semantics><mrow><mfrac><mn>347<\/mn><mn>4<\/mn><\/mfrac><mo>\u2248<\/mo><mn>86,75<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{347}{4}\\approx86,75<\/annotation><\/semantics><\/math>, joten kokonaisosa on 86<br> <math data-latex=\"347-86\\cdot4=3\"><semantics><mrow><mn>347<\/mn><mo>\u2212<\/mo><mn>86<\/mn><mo>\u22c5<\/mo><mn>4<\/mn><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">347-86\\cdot4=3<\/annotation><\/semantics><\/math><br> vastaus: <strong>3<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 6.<\/strong> Ratkaise annetut kohdat.<\/h2>\n\n\n\n<p><strong>a) <\/strong>Etsi luvun 17 kanssa kongruentti luku modulo 12, joka on lukujen 40 ja 50 v\u00e4lill\u00e4.<br><strong>b)<\/strong> Etsi luvun 5 kanssa kongruentti luku modulo 9, joka on lukujen 100 ja 110 v\u00e4lill\u00e4.<br><strong>c)<\/strong> Etsi luvun 253 kanssa kongruentti luku modulo 7, joka on lukujen 3576 ja 3584 v\u00e4lill\u00e4<\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-8&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-8-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-8\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI!<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-8\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-8-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>On ainakin kaksi erilaista tapaa ratkaista teht\u00e4v\u00e4:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Lis\u00e4\u00e4 annettuun lukuun modulon monin kertoja, kunnes p\u00e4\u00e4st\u00e4\u00e4n v\u00e4hint\u00e4\u00e4n annettuun alarajaan. <\/li>\n\n\n\n<li>Selvitet\u00e4\u00e4n, kuinka monta kokonaista kertaa modulo menee yl\u00e4rajan ja luvun erotukseen.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-9&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-9-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-9\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-9\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-9-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a) Vastaus on <strong>41<\/strong>, koska <math data-latex=\"17 + 12 \u22c5 2 = 41\"><semantics><mrow><mn>17<\/mn><mo>+<\/mo><mn>12<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>=<\/mo><mn>41<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">17 + 12 \u22c5 2 = 41<\/annotation><\/semantics><\/math>.<br>b) Vastaus on <strong>104<\/strong>, koska <math data-latex=\"5 + 9 \u22c5 11 = 104\"><semantics><mrow><mn>5<\/mn><mo>+<\/mo><mn>9<\/mn><mo>\u22c5<\/mo><mn>11<\/mn><mo>=<\/mo><mn>104<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5 + 9 \u22c5 11 = 104<\/annotation><\/semantics><\/math>.<br>c) Vastaus on <strong>3\u00a0578<\/strong>, koska <math data-latex=\"\\frac{3584-253}{7}\\approx475{,}857\"><semantics><mrow><mfrac><mrow><mn>3584<\/mn><mo>\u2212<\/mo><mn>253<\/mn><\/mrow><mn>7<\/mn><\/mfrac><mo>\u2248<\/mo><mn>475,857<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3584-253}{7}\\approx475{,}857<\/annotation><\/semantics><\/math>, jonka kokonaisosa on 475. Lis\u00e4t\u00e4\u00e4n siis lukuun 253 modulo 7 yhteens\u00e4 475 kertaa eli <math data-latex=\"253+475\\cdot7=3\u00a0578\"><semantics><mrow><mn>253<\/mn><mo>+<\/mo><mn>475<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>=<\/mo><mn>3578<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">253+475\\cdot7=3&nbsp;578<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 7.<\/strong> Ratkaise ohjelmallisesti. Pyyd\u00e4 input()-funktion avulla arvot.<\/h3>\n\n\n\n<p><strong>a)<\/strong> Toteuta ohjelma, joka antaa nelj\u00e4 (4) lukua, jotka ovat kongruentteja ennalta m\u00e4\u00e4ritetyn toisen luvun ja modulon kanssa.<\/p>\n\n\n\n<p><strong>b) <\/strong>Toteuta ohjelma, joka etsii pienimm\u00e4n luonnollisen luvun, jonka kanssa annettu luku on kongruentti.<\/p>\n\n\n\n<p><strong>c) <\/strong>Toteuta ohjelma, joka selvitt\u00e4\u00e4 onko annettu lauseke kongruentti. \u00a0<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-10&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-10-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-10\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-10\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-10-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"698\" height=\"379\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-24-074525.png\" alt=\"\" class=\"wp-image-2203 size-full\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-24-074525.png 698w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-24-074525-300x163.png 300w\" sizes=\"auto, (max-width: 698px) 100vw, 698px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p>a)<\/p>\n\n\n\n<p><strong>Koodi:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#a\u2261b(mod n)\na = int(input(\"Anna positiivinen kokonaisluku: \"))\nn = int(input(\"Anna positiivinen kokonaisluku: \"))\ni=0\n\nwhile i&lt;4:\n    q =int(input(\"Anna positiivinen kokonaisluku: \"))\n    b = a + n * q\n    print(b)\n    i=i+1\n<\/code><\/pre>\n\n\n\n<p><strong>Tuloste:<\/strong><\/p>\n\n\n\n<p>30<\/p>\n\n\n\n<p>35<\/p>\n\n\n\n<p>40<\/p>\n\n\n\n<p>45<\/p>\n\n\n\n<p><em>Tuloste on saatu, kun a=5, n=5 ja <br>q=5,6,7 ja 8.<\/em><\/p>\n<\/div><\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"647\" height=\"307\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-24-074750.png\" alt=\"\" class=\"wp-image-2204 size-full\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-24-074750.png 647w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-24-074750-300x142.png 300w\" sizes=\"auto, (max-width: 647px) 100vw, 647px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p>b)<\/p>\n\n\n\n<p><strong>Koodi:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a = int(input(\"Anna positiivinen kokonaisluku: \"))\nn= int(input(\"Anna positiivinen kokonaisluku: \"))\n\njakojaannos = a % n\n\nprint(jakojaannos)<\/code><\/pre>\n\n\n\n<p><strong>Tuloste:<\/strong><\/p>\n\n\n\n<p>6<\/p>\n\n\n\n<p><em>Tuloste on saatu, kun a=13 ja n=7.<\/em><\/p>\n<\/div><\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"632\" height=\"499\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-24-084326.png\" alt=\"\" class=\"wp-image-2211 size-full\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-24-084326.png 632w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-24-084326-300x237.png 300w\" sizes=\"auto, (max-width: 632px) 100vw, 632px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p>c)<\/p>\n\n\n\n<p><strong>Koodi:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a = int(input(\"Anna positiivinen kokonaisluku: \"))\nb = int(input(\"Anna positiivinen kokonaisluku: \"))\nn = int(input(\"Anna positiivinen kokonaisluku: \"))\n\nerotus = a - b\nif erotus % n == 0:\n    print(f\"Lauseke {a} \u2261 {b} (mod {n}) on kongruentti.\")\nelse:\n    print(f\"Lauseke {a} \u2261 {b} (mod {n}) ei ole kongruentti.\")<\/code><\/pre>\n\n\n\n<p><strong>Tuloste:<\/strong><\/p>\n\n\n\n<p>Lauseke 5 \u2261 6 (mod 2) ei ole kongruentti.<br>tai<br>Lauseke 24 \u2261 18 (mod 6) on kongruentti.<\/p>\n\n\n\n<p><em>Kongruenssin arvot riippuvat input()-funktiolla annetuista arvoista<\/em>. <\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kongruenssi Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoihin, perus ja vaikeisiin teht\u00e4viin. Teht\u00e4v\u00e4 1. Tutustutaan kongruenssiin. Teht\u00e4v\u00e4 2. Tutki, ovatko annetut lausekkeet totta vai eiv\u00e4t. Perustele vastaus. a) 51\u226116&nbsp;(mod&nbsp;5)51\\equiv16\\ \\left(mod\\ 5\\right)b) 22\u226113&nbsp;(mod&nbsp;3)22\\equiv13\\ \\left(mod\\ 3\\right)c) 36\u226119&nbsp;(mod&nbsp;8)36\\equiv19\\ \\left(mod\\ 8\\right) Teht\u00e4v\u00e4 3. Kirjoita teht\u00e4v\u00e4nantoa<\/p>\n","protected":false},"author":3745,"featured_media":0,"parent":95,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1341","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/1341","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/users\/3745"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/comments?post=1341"}],"version-history":[{"count":23,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/1341\/revisions"}],"predecessor-version":[{"id":2465,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/1341\/revisions\/2465"}],"up":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/95"}],"wp:attachment":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/media?parent=1341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}