{"id":4083,"date":"2026-10-15T07:39:00","date_gmt":"2026-10-15T06:39:00","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/matematik\/dogrusal-diofant-denklemi-hesaplayicisi\/"},"modified":"2026-10-15T07:39:00","modified_gmt":"2026-10-15T06:39:00","slug":"dogrusal-diofant-denklemi-hesaplayicisi","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/dogrusal-diofant-denklemi-hesaplayicisi\/","title":{"rendered":"Do\u011frusal Diofant denklemi hesaplay\u0131c\u0131s\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">ax + by = c denklemini tam say\u0131larda \u00e7\u00f6z\u00fcn<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4083\" data-favorite-title=\"Do\u011frusal Diofant denklemi\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/dogrusal-diofant-denklemi-hesaplayicisi\/\" data-favorite-excerpt=\"ax + by = c do\u011frusal Diofant denklemini tam say\u0131larda \u00e7\u00f6z\u00fcn. a, b ve c katsay\u0131lar\u0131n\u0131 girerek \u00e7\u00f6z\u00fcm olup olmad\u0131\u011f\u0131n\u0131 \u00f6\u011frenin; bir \u00f6zel \u00e7\u00f6z\u00fcm\u00fc ve x = x\u2080 + (b\/g)t, y = y\u2080 \u2212 (a\/g)t bi\u00e7imindeki genel \u00e7\u00f6z\u00fcm\u00fc bulun.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-algebra\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/matematik\/dogrusal-diofant-denklemi-hesaplayicisi\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4083\" data-post=\"4083\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">x&#039;in katsay\u0131s\u0131 (a)<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"xin_katsays_a\" id=\"field-1\" placeholder=\"e.g. 12\" step=\"1\" value=\"12\"\/><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">y&#039;nin katsay\u0131s\u0131 (b)<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"ynin_katsays_b\" id=\"field-2\" placeholder=\"e.g. 18\" step=\"1\" value=\"18\"\/><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Sa\u011f taraf (c)<\/label><div class=\"term\">c<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"sa_taraf_c\" id=\"field-3\" placeholder=\"e.g. 30\" step=\"1\" value=\"30\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4083\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Diofant denklemi sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Tam say\u0131 \u00e7\u00f6z\u00fcm\u00fc var m\u0131?<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Bir \u00e7\u00f6z\u00fcm (x\u2080, y\u2080)<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Genel tam say\u0131 \u00e7\u00f6z\u00fcm\u00fc<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>\u00c7\u00f6z\u00fcm ad\u0131mlar\u0131<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"4083\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Do\u011frusal Diofant denklemi form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ ax + by = c, \\qquad a, b, c \\in \\mathbb{Z} \\]\n\\[ g = \\gcd(a, b) \\]\n\\[ \\text{Tam say\u0131 \u00e7\u00f6z\u00fcm\u00fc vard\u0131r} \\iff g \\mid c \\]\n\\[ x = x_0 + \\frac{b}{g}\\,t, \\qquad y = y_0 - \\frac{a}{g}\\,t, \\qquad t \\in \\mathbb{Z} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(a\\), \\(b\\) \u2014 \\(x\\) ve \\(y\\)\u2019nin tam say\u0131 katsay\u0131lar\u0131<\/li>\n<li>\\(c\\) \u2014 e\u015fitli\u011fin sa\u011f taraf\u0131ndaki tam say\u0131<\/li>\n<li>\\(g = \\gcd(a, b)\\) \u2014 katsay\u0131lar\u0131n en b\u00fcy\u00fck ortak b\u00f6leni<\/li>\n<li>\\((x_0, y_0)\\) \u2014 \\(g = s\\,a + t\\,b\\) B\u00e9zout \u00f6zde\u015fli\u011findeki katsay\u0131lar\u0131n \\(c\/g\\) ile \u00e7arp\u0131lmas\u0131yla bulunan bir \u00f6zel \u00e7\u00f6z\u00fcm<\/li>\n<li>\\(t\\) \u2014 t\u00fcm \u00e7\u00f6z\u00fcmleri veren, istenilen tam say\u0131 de\u011ferini alabilen parametre<\/li>\n<\/ul>\n<p>Denklemin tam say\u0131 \u00e7\u00f6z\u00fcm\u00fc olmas\u0131 i\u00e7in ve ancak bunun i\u00e7in \\(\\gcd(a,b)\\), \\(c\\)\u2019yi b\u00f6lmelidir. Bu ko\u015ful sa\u011fland\u0131\u011f\u0131nda sonsuz say\u0131da \u00e7\u00f6z\u00fcm vard\u0131r: Bir \\((x_0, y_0)\\) \u00e7\u00f6z\u00fcm\u00fcnden ba\u015flayarak \\(x\\)\u2019e \\(b\/g\\) ekleyip \\(y\\)\u2019den \\(a\/g\\) \u00e7\u0131karmak, ayn\u0131 i\u015flem \\(t\\) kez uyguland\u0131\u011f\u0131nda di\u011fer b\u00fct\u00fcn \u00e7\u00f6z\u00fcmleri verir.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Do\u011frusal Diofant denklemi: hesaplama \u00f6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \\(12x + 18y = 30\\) denklemini tam say\u0131larda \u00e7\u00f6z\u00fcn (hesaplay\u0131c\u0131n\u0131n varsay\u0131lan de\u011ferleri).<\/p>\n<p>\\[ \\gcd(12, 18): \\quad 18 = 1 \\cdot 12 + 6, \\quad 12 = 2 \\cdot 6 + 0 \\implies \\gcd(12, 18) = 6 \\]<\/p>\n<p>\\[ 6 \\mid 30 \\implies \\text{\u00e7\u00f6z\u00fcmler vard\u0131r} \\]<\/p>\n<p>\\[ \\text{B\u00e9zout: } 6 = (-1) \\cdot 12 + 1 \\cdot 18, \\qquad \\frac{c}{g} = \\frac{30}{6} = 5 \\]<\/p>\n<p>\\[ x_0 = -1 \\cdot 5 = -5, \\qquad y_0 = 1 \\cdot 5 = 5 \\]<\/p>\n<p>\\[ 12 \\cdot (-5) + 18 \\cdot 5 = -60 + 90 = 30 \\;\\checkmark \\]<\/p>\n<p>\\(x_0\\) de\u011feri \\(0 \\le x &lt; |b\/g| = 3\\) aral\u0131\u011f\u0131na kayd\u0131r\u0131ld\u0131\u011f\u0131nda, \\(12 \\cdot 1 + 18 \\cdot 1 = 30\\) oldu\u011fundan e\u015fde\u011fer \u00f6zel \u00e7\u00f6z\u00fcm \\((1, 1)\\) elde edilir.<\/p>\n<p><strong>Sonu\u00e7:<\/strong> T\u00fcm tam say\u0131 \u00e7\u00f6z\u00fcmleri, \\(t\\) herhangi bir tam say\u0131 olmak \u00fczere \\(x = 1 + 3t\\), \\(y = 1 - 2t\\) bi\u00e7imindedir. \u00d6rne\u011fin \\((1, 1)\\), \\((4, -1)\\) ve \\((-2, 3)\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>\\(x\\)\u2019in tam say\u0131 katsay\u0131s\u0131n\u0131 <strong>x\u2019in katsay\u0131s\u0131 (a)<\/strong> alan\u0131na girin.<\/li>\n<li>\\(y\\)\u2019nin tam say\u0131 katsay\u0131s\u0131n\u0131 <strong>y\u2019nin katsay\u0131s\u0131 (b)<\/strong> alan\u0131na girin.<\/li>\n<li>E\u015fitli\u011fin sa\u011f taraf\u0131ndaki say\u0131y\u0131 <strong>Sa\u011f taraf (c)<\/strong> alan\u0131na girin.<\/li>\n<li>Sonu\u00e7 b\u00f6l\u00fcmlerini inceleyin: <strong>Tam say\u0131 \u00e7\u00f6z\u00fcm\u00fc var m\u0131?<\/strong> b\u00f6l\u00fcm\u00fcnde \\(\\gcd(a,b)\\)\u2019nin \\(c\\)\u2019yi b\u00f6l\u00fcp b\u00f6lmedi\u011fini; <strong>Bir \u00e7\u00f6z\u00fcm (x\u2080, y\u2080)<\/strong> b\u00f6l\u00fcm\u00fcnde do\u011frulanm\u0131\u015f bir \u00f6zel \u00e7\u00f6z\u00fcm\u00fc; <strong>Genel tam say\u0131 \u00e7\u00f6z\u00fcm\u00fc<\/strong> b\u00f6l\u00fcm\u00fcnde \\(t\\) parametresiyle t\u00fcm \u00e7\u00f6z\u00fcmleri; <strong>\u00c7\u00f6z\u00fcm ad\u0131mlar\u0131<\/strong> b\u00f6l\u00fcm\u00fcnde ise \u00d6klid algoritmas\u0131n\u0131, B\u00e9zout katsay\u0131lar\u0131n\u0131 ve \u00e7\u00f6z\u00fcm\u00fcn gerek\u00e7esini g\u00f6rebilirsiniz.<\/li>\n<\/ol>\n<p>\u00dc\u00e7 alana da tam say\u0131 girmelisiniz; say\u0131lar pozitif, negatif veya s\u0131f\u0131r olabilir. Tam say\u0131 olmayan bir de\u011fer girerseniz hesaplay\u0131c\u0131 sizden tam say\u0131 ister. \u00c7\u00fcnk\u00fc Diofant denklemlerinde tan\u0131m gere\u011fi yaln\u0131zca tam say\u0131 \u00e7\u00f6z\u00fcmler aran\u0131r.<\/p>\n<h2>Do\u011frusal Diofant denklemi nedir?<\/h2>\n<p>Diofant denklemi, \u00e7\u00f6z\u00fcmleri tam say\u0131 olmak zorunda olan denklemdir. En basit t\u00fcr\u00fc olan \\(ax + by = c\\) do\u011frusal Diofant denkleminde, e\u015fitli\u011fi tam olarak sa\u011flayan t\u00fcm \\((x, y)\\) tam say\u0131 \u00e7iftleri aran\u0131r; kesirli veya ondal\u0131k de\u011ferlere izin verilmez. Bu denklemler, belirli de\u011ferdeki madeni paralar, \u00fcr\u00fcn dolu kutular, insanlar veya karolar gibi b\u00f6l\u00fcnemeyen \u015feylerin say\u0131ld\u0131\u011f\u0131 durumlarda kar\u015f\u0131m\u0131za \u00e7\u0131kar.<\/p>\n<p>Temel nokta, \u00e7\u00f6z\u00fcm\u00fcn hangi ko\u015fulda var oldu\u011fudur: \\(ax + by\\) her zaman \\(\\gcd(a, b)\\)\u2019nin kat\u0131 oldu\u011fundan \\(c\\) de \\(\\gcd(a, b)\\)\u2019nin kat\u0131 olmal\u0131d\u0131r. \u00d6rne\u011fin \\(6x + 10y\\) her zaman \u00e7ifttir; dolay\u0131s\u0131yla ne kadar u\u011fra\u015f\u0131rsan\u0131z u\u011fra\u015f\u0131n \\(6x + 10y = 7\\) denkleminin tam say\u0131 \u00e7\u00f6z\u00fcm\u00fcn\u00fc bulamazs\u0131n\u0131z. Ko\u015ful sa\u011fland\u0131\u011f\u0131nda B\u00e9zout \u00f6zde\u015fli\u011fi en az bir \u00e7\u00f6z\u00fcm\u00fcn varl\u0131\u011f\u0131n\u0131 garanti eder; geni\u015fletilmi\u015f \u00d6klid algoritmas\u0131 da bu \u00e7\u00f6z\u00fcm\u00fc verimli bi\u00e7imde bulur.<\/p>\n<p>Sonucu \u015f\u00f6yle yorumlayabilirsiniz: \u00c7\u00f6z\u00fcm varsa, bir aritmetik dizi boyunca s\u0131ralanan sonsuz say\u0131da \u00e7\u00f6z\u00fcm vard\u0131r. \\(x = x_0 + (b\/g)t\\), \\(y = y_0 - (a\/g)t\\) genel \u00e7\u00f6z\u00fcm\u00fc bunlar\u0131n tamam\u0131n\u0131 g\u00f6sterir. \\(t\\) bir art\u0131r\u0131ld\u0131\u011f\u0131nda \\(x\\), \\(b\/g\\) kadar artarken \\(y\\), \\(a\/g\\) kadar azal\u0131r; b\u00f6ylece \\(ax + by\\) de\u011fi\u015fmez. Belirli bir aral\u0131ktaki \u00e7\u00f6z\u00fcmleri, \u00f6rne\u011fin negatif olmayanlar\u0131 ar\u0131yorsan\u0131z birka\u00e7 \\(t\\) de\u011feri deneyip ko\u015fulunuza uyanlar\u0131 se\u00e7in.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlamalar ve ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Yaln\u0131zca tam say\u0131lar.<\/strong> Katsay\u0131lar tam say\u0131 olmal\u0131d\u0131r; denklem rasyonel veya reel say\u0131larda \u00e7\u00f6z\u00fclmez. Reel say\u0131larda \\(a\\) ya da \\(b\\) s\u0131f\u0131rdan farkl\u0131ysa \\(ax + by = c\\) denkleminin her zaman \u00e7\u00f6z\u00fcm\u00fc vard\u0131r. Problemi ilgin\u00e7 k\u0131lan, tam say\u0131 ko\u015fuludur.<\/li>\n<li><strong>Say\u0131 b\u00fcy\u00fckl\u00fc\u011f\u00fc s\u0131n\u0131r\u0131.<\/strong> Hesaplamada standart aritmetik kullan\u0131l\u0131r. Hassasiyet sorunlar\u0131n\u0131 \u00f6nlemek i\u00e7in katsay\u0131lar\u0131 g\u00fcvenli tam say\u0131 aral\u0131\u011f\u0131nda, yakla\u015f\u0131k 15 basama\u011f\u0131 a\u015fmayacak \u015fekilde tutun.<\/li>\n<li><strong>\u00d6zel durumlar da ele al\u0131n\u0131r.<\/strong> \\(a = b = 0\\) ise denklem ya her zaman do\u011frudur (\\(c = 0\\) oldu\u011funda her \u00e7ift \u00e7\u00f6z\u00fcmd\u00fcr) ya da hi\u00e7bir zaman do\u011fru de\u011fildir. Katsay\u0131lardan yaln\u0131zca biri s\u0131f\u0131rsa denklem tek de\u011fi\u015fkenli h\u00e2le gelir ve hesaplay\u0131c\u0131 bunu do\u011frudan \u00e7\u00f6zer.<\/li>\n<li><strong>Herhangi bir \u00f6zel \u00e7\u00f6z\u00fcm kullan\u0131labilir.<\/strong> \\((x_0, y_0)\\) \u00e7ifti tek de\u011fildir. Hesaplay\u0131c\u0131 bu \u00e7ifti \\(0 \\le x_0 &lt; |b\/g|\\) ko\u015fulunu sa\u011flayan k\u00fc\u00e7\u00fck de\u011ferli bir bi\u00e7ime kayd\u0131r\u0131r; ancak se\u00e7ilen \u00f6zel \u00e7\u00f6z\u00fcm ne olursa olsun \\(t\\) parametresiyle ayn\u0131 tam \u00e7\u00f6z\u00fcm k\u00fcmesi elde edilir.<\/li>\n<li><strong>Cevab\u0131n\u0131z\u0131 kontrol edin.<\/strong> \u00d6zel \u00e7\u00f6z\u00fcm\u00fc denklemde yerine koyup \\(a x_0 + b y_0\\) de\u011ferinin \\(c\\)\u2019ye e\u015fit oldu\u011funu her zaman do\u011frulay\u0131n. Hesaplay\u0131c\u0131 bu kontrol\u00fc sonu\u00e7ta sizin i\u00e7in yapar.<\/li>\n<\/ul>\n<p>Probleminizde tek denklem yerine \\(ax + by = c\\), \\(dx + ey = f\\) gibi iki do\u011frusal denklemden olu\u015fan bir sistem varsa EBOB ile b\u00f6l\u00fcnebilme ko\u015fulu yerine <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/yok-etme-yontemi\/\">yok etme y\u00f6ntemi<\/a> kullan\u0131l\u0131r. Diofant denklemlerine dayanan ak\u0131l y\u00fcr\u00fctme, tam say\u0131 de\u011ferli iki b\u00fcy\u00fckl\u00fc\u011f\u00fcn sabit oranda artt\u0131\u011f\u0131 <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/dogru-oranti\/\">do\u011fru orant\u0131<\/a> gibi konular\u0131n da temelinde yer al\u0131r. Ayr\u0131ca matematik yar\u0131\u015fmalar\u0131nda ve say\u0131lar teorisi problemlerinde s\u0131k kullan\u0131lan klasik bir ara\u00e7t\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>ax + by = c do\u011frusal Diofant denklemini tam say\u0131larda \u00e7\u00f6z\u00fcn. a, b ve c katsay\u0131lar\u0131n\u0131 girerek \u00e7\u00f6z\u00fcm olup olmad\u0131\u011f\u0131n\u0131 \u00f6\u011frenin; bir \u00f6zel \u00e7\u00f6z\u00fcm\u00fc ve x = x\u2080 + (b\/g)t, y = y\u2080 \u2212 (a\/g)t bi\u00e7imindeki genel \u00e7\u00f6z\u00fcm\u00fc bulun.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[16],"class_list":["post-4083","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-cebir"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4083","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=4083"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4083\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4083"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4083"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4083"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}