{"id":98547,"date":"2025-10-17T03:00:27","date_gmt":"2025-10-16T21:00:27","guid":{"rendered":"https:\/\/sarakhon.com\/?p=98547"},"modified":"2025-10-16T16:42:11","modified_gmt":"2025-10-16T10:42:11","slug":"%e0%a6%aa%e0%a7%8d%e0%a6%b0%e0%a6%be%e0%a6%9a%e0%a7%80%e0%a6%a8-%e0%a6%ad%e0%a6%be%e0%a6%b0%e0%a6%a4%e0%a7%87-%e0%a6%97%e0%a6%a3%e0%a6%bf%e0%a6%a4%e0%a6%9a%e0%a6%b0%e0%a7%8d%e0%a6%9a%e0%a6%be-304","status":"publish","type":"post","link":"https:\/\/sarakhon.com\/?p=98547","title":{"rendered":"\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e9\u09e6\u09ee)"},"content":{"rendered":"<p><strong>\u0986\u09ae\u09b0\u09be by=ax+c \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09aa\u09cd\u09b0\u09a5\u09ae \u0986\u09b0\u09cd\u09af\u09ad\u099f\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a3\u09be\u09b2\u09c0\u09a4\u09c7 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u09c7 \u09a6\u09c7\u0996\u09be\u099a\u09cd\u099b\u09bf\u0964 \u0985\u09ac\u09b6\u09cd\u09af \u098f\u0996\u09be\u09a8\u09c7 \u09eb \u098f\u09ac\u0982 b \u09ae\u09cc\u09b2\u09bf\u0995 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09a7\u09b0\u09be \u09b9\u09df\u09c7\u099b\u09c7\u0964<\/strong><\/p>\n<p>\u098f\u0996\u09a8..<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-98548 aligncenter\" src=\"https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/10\/9-16.jpg\" alt=\"\" width=\"362\" height=\"257\" \/><\/p>\n<p>\u09a4\u09be\u09b9\u09b2\u09c7 (\u09af\u0996\u09a8 a &lt; b \u09a4\u0996\u09a8 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987 q = 0R<sub>1 <\/sub>= a ) \u09a6\u09c7\u0996\u09be \u09af\u09be\u099a\u09cd\u099b\u09c7<br \/>\na = bq +R<sub>1<\/sub><\/p>\n<p>b = R<sub>1<\/sub>q<sub>1<\/sub> +R<sub>1<\/sub><\/p>\n<p>r m &#8211; 1 =r m-1 q m-1 +r m<\/p>\n<p>r m &#8211; 1 =r m q m +r m+1<\/p>\n<p>a-\u098f\u09b0 \u09ae\u09be\u09a8 by = ax + c \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf\u09a4\u09c7 \u09ac\u09b8\u09be\u09b2\u09c7 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df by = (bq + r<sub>1<\/sub>} x) + c \u0985\u09a4\u098f\u09ac y = qx + y<sub>1<\/sub> \u098f\u0996\u09be\u09a8\u09c7 by<sub>1<\/sub> = r<sub>1<\/sub>x + c<\/p>\n<p>\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 a = bq + r<sub>1<\/sub> \u09ae\u09be\u09a8 \u09ac\u09b8\u09be\u09a8\u09cb\u09b0 \u09aa\u09b0 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987 y= qx +y 1 &#8230;&#8230;&#8230;.[1] \u098f\u0996\u09a8 b_{v} = ax + c \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09df\u09c7 \u09a6\u09be\u0981\u09dc\u09be\u09df by =r 1 x+c&#8230;&#8230;&#8230;&#8230;..[1.1]<\/p>\n<p>\u0986\u09ac\u09be\u09b0 \u09af\u09c7\u09b9\u09c7\u09a4\u09c1 b = r<sub>1<\/sub>q<sub>1<\/sub> + r<sub>2<\/sub><\/p>\n<p>\u09a0\u09bf\u0995 \u098f\u0995\u0987\u09ad\u09be\u09ac\u09c7 \u09ac\u09b8\u09be\u09b2\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987 x = q<sub>1 <\/sub>y + x<sub>1<\/sub> \u09a4\u09be\u09b9\u09b2\u09c7 [1.1] \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u0986\u0995\u09be\u09b0 \u09a7\u09be\u09b0\u09a3 \u0995\u09b0\u09c7 \u098f\u0987\u09b0\u09c2\u09aa \u09b9\u09df<\/p>\n<p>r<sub>1<\/sub>x<sub>1<\/sub> = r<sub>2 <\/sub>y<sub>1<\/sub> &#8211; c [1.2].<\/p>\n<p>\u098f\u0987\u09ad\u09be\u09ac\u09c7 \u09af\u09a6\u09bf \u098f\u0987 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf \u0985\u09a8\u09c1\u09b8\u09b0\u09a3 \u0995\u09b0\u09be \u09af\u09be\u09df \u09a4\u09be\u09b9\u09b2\u09c7 \u0986\u09ae\u09b0\u09be \u09a8\u09bf\u09ae\u09cd\u09a8\u09b2\u09bf\u0996\u09bf\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09c2\u09b9 \u09aa\u09be\u0987\u0964<\/p>\n<p>[1] y = qx + y<sub>1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 bY1 =R1 x + c\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [1-1]<\/sub><\/p>\n<p>[2] x = q<sub>1<\/sub>y + x<sub>1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/sub>r<sub>1<\/sub>x<sub>1<\/sub> = r<sub>2<\/sub>y<sub>1 <\/sub>&#8211; c\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0[1.2]<\/p>\n<p>[3] y<sub>1\u00a0<\/sub> = q<sub>2 <\/sub>x<sub>1<\/sub>+ y<sub>2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/sub>r<sub>2\u00a0<\/sub>y<sub>2\u00a0<\/sub> = r<sub>3 <\/sub>x<sub>1<\/sub> + c\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0[1.3]<\/p>\n<p>[4] x<sub>1<\/sub> = q<sub>3 <\/sub>y<sub>2<\/sub> + x<sub>2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/sub>r<sub>3<\/sub>x<sub>2\u00a0<\/sub> = r<sub>4 <\/sub>y<sub>2\u00a0<\/sub> &#8211; c\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0[1.4]<\/p>\n<p>&#8230;<\/p>\n<p>[25] x s &#8211; 1 =q 2s-1 y s +x s r y, n &#8211; 1 x s =r 2,n y s -c\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [1&#8217;2s]<\/p>\n<p>[2s + 1] y s =q 2 x s +y s + 1 r 3, y y s+1 =r 2,s+1 x s +c\u00a0 \u00a0 \u00a0 \u00a0 [12s+1]<\/p>\n<p>\u098f\u0996\u09a8 \u0986\u09ae\u09b0\u09be \u09a6\u09c1\u099f\u09bf \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09be\u09ac (\u09e7) \u09aa\u09be\u09b0\u09b8\u09cd\u09aa\u09b0\u09bf\u0995 \u09ad\u09be\u0997 \u0995\u09b0\u09be\u09b0 \u09ab\u09b2\u09c7 \u098f\u09ae\u09a8 \u098f\u0995 \u099c\u09be\u09df\u0997\u09be\u09df \u09aa\u09cc\u0981\u099b\u09be\u09ac \u09af\u09c7\u0996\u09be\u09a8\u09c7 \u0995\u09cb\u09a8 \u0985\u09ac\u09b6\u09bf\u09b7\u09cd\u099f \u09a5\u09be\u0995\u09ac\u09c7 \u09a8\u09be\u0964 (\u09e8) \u0985\u09a5\u09ac\u09be \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09ad\u09be\u0997\u09ab\u09b2 \u09aa\u09be\u09ac\u09be\u09b0 \u09aa\u09b0 \u0986\u09ae\u09b0\u09be \u0986\u09b0 \u0985\u0997\u09cd\u09b0\u09b8\u09b0 \u09b9\u09ac\u09cb \u09a8\u09be\u0964 \u09af\u09c7 \u0995\u09cb\u09a8 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u0987 \u09b9\u09cb&#8217;\u0995 \u0986\u09ae\u09b0\u09be \u09aa\u09cd\u09b0\u09a5\u09ae \u09ad\u09be\u0997\u09ab\u09b2\u099f\u09bf\u0995\u09c7 \u09ac\u09be\u09a6 \u09a6\u09c7\u09ac\u09cb\u0964<\/p>\n<p>(\u09e7.) \u09af\u0996\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af \u0985\u09ac\u09b6\u09bf\u09b7\u09cd\u099f \u09a5\u09be\u0995\u099b\u09c7: \u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u09eb \u098f\u09ac\u0982 b \u09aa\u09be\u09b0\u09b8\u09cd\u09aa\u09b0\u09bf\u0995 \u09ae\u09cc\u09b2\u09bf\u0995\u0964 \u0985\u09a4\u098f\u09ac \u09b6\u09c7\u09b7 \u09ad\u09be\u0997\u09b6\u09c7\u09b7\u09c7\u09b0 \u09a0\u09bf\u0995 \u09aa\u09c2\u09b0\u09cd\u09ac\u09c7\u09b0 \u09ad\u09be\u0997\u09b6\u09c7\u09b7 \u098f\u0995 \u09b9\u09ac\u09c7\u0964<\/p>\n<p><strong>(\u099a\u09b2\u09ac\u09c7)<\/strong><\/p>\n<p class=\"single-page-title\"><strong>\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e9\u09e6\u09ed)<\/strong><\/p>\n<blockquote class=\"wp-embedded-content\" data-secret=\"y2JmHCSHyy\"><p><a href=\"https:\/\/sarakhon.com\/?p=97613\">\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e9\u09e6\u09ed)<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e9\u09e6\u09ed)&#8221; &#8212; Sarakhon \u0964 \u09b8\u09be\u09b0\u09be\u0995\u09cd\u09b7\u09a3\" src=\"https:\/\/sarakhon.com\/?p=97613&#038;embed=true#?secret=WB7YmZaJAZ#?secret=y2JmHCSHyy\" data-secret=\"y2JmHCSHyy\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0986\u09ae\u09b0\u09be by=ax+c \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09aa\u09cd\u09b0\u09a5\u09ae \u0986\u09b0\u09cd\u09af\u09ad\u099f\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a3\u09be\u09b2\u09c0\u09a4\u09c7 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u09c7 \u09a6\u09c7\u0996\u09be\u099a\u09cd\u099b\u09bf\u0964 \u0985\u09ac\u09b6\u09cd\u09af \u098f\u0996\u09be\u09a8\u09c7 \u09eb \u098f\u09ac\u0982 b \u09ae\u09cc\u09b2\u09bf\u0995 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09a7\u09b0\u09be \u09b9\u09df\u09c7\u099b\u09c7\u0964 \u098f\u0996\u09a8.. \u09a4\u09be\u09b9\u09b2\u09c7 (\u09af\u0996\u09a8 a &lt; b \u09a4\u0996\u09a8 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987 q = 0R1 = a ) \u09a6\u09c7\u0996\u09be \u09af\u09be\u099a\u09cd\u099b\u09c7 a = bq +R1 b = R1q1 +R1 r m &#8211; 1 =r m-1 q m-1 +r m r m [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":98549,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[38,17],"tags":[],"location":[],"class_list":["post-98547","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-38","category-17"],"cmb2":{"heading_information":{"sub_title":""},"reporter_information":{"video":"","reporter_name":"\u09aa\u09cd\u09b0\u09a6\u09c0\u09aa \u0995\u09c1\u09ae\u09be\u09b0 \u09ae\u099c\u09c1\u09ae\u09a6\u09be\u09b0"},"audio_information":{"audio_link":"","audio_link_id":""},"seo_information":{"meta_keyword":""}},"_links":{"self":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/98547","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=98547"}],"version-history":[{"count":2,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/98547\/revisions"}],"predecessor-version":[{"id":98551,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/98547\/revisions\/98551"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/media\/98549"}],"wp:attachment":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=98547"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=98547"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=98547"},{"taxonomy":"location","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Flocation&post=98547"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}