{"id":93358,"date":"2025-10-01T03:00:17","date_gmt":"2025-09-30T21:00:17","guid":{"rendered":"https:\/\/sarakhon.com\/?p=93358"},"modified":"2025-09-30T17:03:37","modified_gmt":"2025-09-30T11:03:37","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-291","status":"publish","type":"post","link":"https:\/\/sarakhon.com\/?p=93358","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-\u09e8\u09ef\u09eb)"},"content":{"rendered":"<p><em>\u09ad\u09be\u09b0\u09a4\u09c0\u09df \u098f\u0995\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u0985\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u09ac\u09cd\u09af\u09be\u09aa\u0995 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8 \u098f\u09ac\u0982 \u09a4\u09bf\u09a8\u09bf \u0995\u09cd\u09af\u09c7&#8217;\u09b0 \u09ae\u09a8\u09cd\u09a4\u09ac\u09cd\u09af\u0995\u09c7 \u09a7\u09c2\u09b2\u09bf\u09b8\u09be\u09ce \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964 <\/em><\/p>\n<p><strong>\u0986\u09b0\u09cd\u09af\u09ad\u099f\u09c7\u09b0 \u098f\u0995 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u098f\u09a8. \u0995\u09c7. \u09ae\u099c\u09c1\u09ae\u09a6\u09be\u09b0 \u09a4\u09be\u0981\u09b0 \u0997\u09ac\u09c7\u09b7\u09a3\u09be\u09ae\u09c2\u09b2\u0995 \u09aa\u09cd\u09b0\u09ac\u09a8\u09cd\u09a7\u09c7 (Aryabhatas rule in relation to the indeterminate equation of the first degree, B. C. M. S. No.-3, 1911-12, pp 11-19) \u09ac\u09b2\u09c7\u099b\u09c7\u09a8, \u0986\u09b0\u09cd\u09af\u09ad\u099f \u0995\u0996\u09a8\u0987 \u0987\u0989\u0995\u09cd\u09b2\u09bf\u09a1 \u09ac\u09be \u0985\u09a8\u09cd\u09af\u09be\u09a8\u09cd\u09af \u0997\u09cd\u09b0\u09c0\u0995 \u09ac\u09be \u0986\u09b2\u09c7\u0995\u099c\u09be\u09a8\u09cd\u09a6\u09cd\u09b0\u09c0\u09df \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6\u09a6\u09c7\u09b0 \u09a8\u09bf\u0995\u099f \u098f \u09ac\u09cd\u09af\u09be\u09aa\u09be\u09b0\u09c7 \u098b\u09a3\u09c0 \u099b\u09bf\u09b2\u09c7\u09a8 \u09a8\u09be\u0964 \u098f\u09a8. \u0995\u09c7. \u09ae\u099c\u09c1\u09ae\u09a6\u09be\u09b0 \u098f \u09ac\u09cd\u09af\u09be\u09aa\u09be\u09b0\u09c7 \u0995\u09cd\u09af\u09c7, \u09b9\u09be\u0981\u09a5 \u09aa\u09cd\u09b0\u09ae\u09c1\u0996\u09a6\u09c7\u09b0 \u09ac\u09bf\u099a\u09be\u09b0 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3\u0995\u09c7 \u09b8\u09ae\u09be\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964 <\/strong><\/p>\n<p>\u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u09ad\u09be\u09b8\u09cd\u0995\u09b0\u09be\u099a\u09be\u09b0\u09cd\u09af\u09c7\u09b0 \u09b2\u09c0\u09b2\u09be\u09ac\u09a4\u09c0\u09b0 \u0987\u0982\u09b0\u09be\u099c\u09c0 \u0985\u09a8\u09c1\u09ac\u09be\u09a6 \u0995\u09cb\u09b2\u09c7\u0995\u09cd\u09b0\u0995 \u09b8\u09be\u09b9\u09c7\u09ac\u09c7\u09b0 \u0995\u09b0\u09c7\u09a8\u0964 \u098f\u099f\u09bf \u0986\u09ac\u09be\u09b0 \u09b9\u09be\u09b0\u09be\u09a3\u099a\u09a8\u09cd\u09a6\u09cd\u09b0 \u09ac\u09cd\u09af\u09be\u09a8\u09be\u09b0\u09cd\u099c\u09bf &#8216;\u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u09b8\u0982\u09b8\u09cd\u0995\u09b0\u09a3\u09c7 \u0995\u09bf\u099b\u09c1\u099f\u09be \u099f\u09c0\u0995\u09be \u09af\u09cb\u0997 \u0995\u09b0\u09c7\u09a8 \u098f\u09ac\u0982 \u098f\u0987 \u099f\u09be\u0995\u09be\u09a4\u09c7 \u09b9\u09be\u09b0\u09be\u09a3\u099a\u09a8\u09cd\u09a6\u09cd\u09b0 \u09ac\u09cd\u09af\u09be\u09a8\u09be\u09bf \u09ac\u09b2\u09c7\u099b\u09c7\u09a8, \u09ac\u09bf\u09a4\u09a4 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6\u09c7\u09b0 \u0985\u09ad\u09bf\u09b8\u09be\u09b0\u09bf\u09a4\u09cd\u09ac \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 (Convergents of the Conti-nued fraction) \u09aa\u09cd\u09b0\u099a\u09cd\u099b\u09a8\u09cd\u09a8\u09ad\u09be\u09ac\u09c7 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u09ad\u09be\u09b8\u09cd\u0995\u09b0\u09be\u099a\u09be\u09b0\u09cd\u09af \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964 \u09a8\u09b2\u09bf\u09a8\u09c0 \u09ac\u09bf\u09b9\u09be\u09b0\u09c0 \u09ae\u09bf\u09a4\u09cd\u09b0 \u09a4\u09be\u0981\u09b0 \u09a6\u09c1\u099f\u09bf \u09aa\u09cd\u09b0\u09ac\u09a8\u09cd\u09a7\u09c7 ([a] Modern Review, Vol 18, June&#8211;Dec., 1913. P 506-508 on Indeterminate equations of the first degree,<br \/>\n[b] Modern Review, Vol xvii, no 1, P-75) \u0995\u09cb&#8217;\u09b0 \u09ae\u09a8\u09cd\u09a4\u09ac\u09cd\u09af\u09c7\u09b0 \u09b8\u09ae\u09be\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8 \u098f\u09ac\u0982 \u09ad\u09be\u09b0\u09a4\u09c0\u09df \u098f\u0995 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u09ac\u09cd\u09af\u09be\u09aa\u0995 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964<\/p>\n<p>\u09b8\u09be\u09b0\u09a6\u09be\u0995\u09be\u09a8\u09cd\u09a4 \u0997\u09be\u0999\u09cd\u0997\u09c1\u09b2\u09c0 \u09a4\u09be\u0981\u09b0 \u09aa\u09cd\u09b0\u09ac\u09a8\u09cd\u09a7 \u09b8\u09ae\u09c2\u09b9\u09c7 [(a) India&#8217;s Contribution to the theory of Indeterminate equation of the first degree, Journal of the Indian Mathematical Society, Vol 19, 1932. pp 110-120, 129-140, 153-169. (ii) Journal of the Bihar and Orissa Research Society, March 1926, (iii) American Mathematical monthly, Vol 34, 37, (iv) Isis, Vol 12, 1929], \u09ad\u09be\u09b0\u09a4\u09c0\u09df \u098f\u0995\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u0985\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u09ac\u09cd\u09af\u09be\u09aa\u0995 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8 \u098f\u09ac\u0982 \u09a4\u09bf\u09a8\u09bf \u0995\u09cd\u09af\u09c7&#8217;\u09b0 \u09ae\u09a8\u09cd\u09a4\u09ac\u09cd\u09af\u0995\u09c7 \u09a7\u09c2\u09b2\u09bf\u09b8\u09be\u09ce \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964 \u09a4\u09be\u099b\u09be\u09dc\u09be\u0993 \u09ac\u09b2\u09c7\u099b\u09c7\u09a8 \u09ad\u09be\u09b0\u09a4\u09c0\u09df \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf\u09a4\u09c7 \u0997\u09cd\u09b0\u09c0\u0995 \u09ac\u09be \u099a\u09c0\u09a8\u09be \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf\u09b0 \u09aa\u09cd\u09b0\u09ad\u09be\u09ac \u09a8\u09c7\u0987\u0964 \u09aa\u09cd\u09b0\u09ac\u09cb\u09a7 \u099a\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b8\u09c7\u09a8\u0997\u09c1\u09aa\u09cd\u09a4 \u098f\u09ac\u0982 \u09a1\u09ac\u09cd\u09b2\u09bf\u0989. \u0987. \u0995\u09cd\u09b2\u09be\u09b0\u09cd\u0995 \u09b6\u09c1\u09a7\u09c1\u09ae\u09be\u09a4\u09cd\u09b0 \u0986\u09b0\u09cd\u09af\u09ad\u099f\u09c0\u09df\u09c7\u09b0 \u0987\u0982\u09b0\u09be\u099c\u09c0 \u0985\u09a8\u09c1\u09ac\u09be\u09a6 \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964<\/p>\n<p><strong>(\u099a\u09b2\u09ac\u09c7)<\/strong><\/p>\n<h4 class=\"single-page-title\">\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-\u09e8\u09ef\u09ea)<\/h4>\n<blockquote class=\"wp-embedded-content\" data-secret=\"0Hw3MJXqnQ\"><p><a href=\"https:\/\/sarakhon.com\/?p=93004\">\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-\u09e8\u09ef\u09ea)<\/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-\u09e8\u09ef\u09ea)&#8221; &#8212; Sarakhon \u0964 \u09b8\u09be\u09b0\u09be\u0995\u09cd\u09b7\u09a3\" src=\"https:\/\/sarakhon.com\/?p=93004&#038;embed=true#?secret=H0auM6OxvU#?secret=0Hw3MJXqnQ\" data-secret=\"0Hw3MJXqnQ\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u09ad\u09be\u09b0\u09a4\u09c0\u09df \u098f\u0995\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u0985\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u09ac\u09cd\u09af\u09be\u09aa\u0995 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8 \u098f\u09ac\u0982 \u09a4\u09bf\u09a8\u09bf \u0995\u09cd\u09af\u09c7&#8217;\u09b0 \u09ae\u09a8\u09cd\u09a4\u09ac\u09cd\u09af\u0995\u09c7 \u09a7\u09c2\u09b2\u09bf\u09b8\u09be\u09ce \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964 \u0986\u09b0\u09cd\u09af\u09ad\u099f\u09c7\u09b0 \u098f\u0995 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u098f\u09a8. \u0995\u09c7. \u09ae\u099c\u09c1\u09ae\u09a6\u09be\u09b0 \u09a4\u09be\u0981\u09b0 \u0997\u09ac\u09c7\u09b7\u09a3\u09be\u09ae\u09c2\u09b2\u0995 \u09aa\u09cd\u09b0\u09ac\u09a8\u09cd\u09a7\u09c7 (Aryabhatas rule in relation to the indeterminate equation of the first degree, B. C. M. S. No.-3, 1911-12, pp 11-19) \u09ac\u09b2\u09c7\u099b\u09c7\u09a8, \u0986\u09b0\u09cd\u09af\u09ad\u099f \u0995\u0996\u09a8\u0987 \u0987\u0989\u0995\u09cd\u09b2\u09bf\u09a1 \u09ac\u09be \u0985\u09a8\u09cd\u09af\u09be\u09a8\u09cd\u09af \u0997\u09cd\u09b0\u09c0\u0995 \u09ac\u09be \u0986\u09b2\u09c7\u0995\u099c\u09be\u09a8\u09cd\u09a6\u09cd\u09b0\u09c0\u09df \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6\u09a6\u09c7\u09b0 [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":93359,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[38,17],"tags":[],"location":[],"class_list":["post-93358","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\/93358","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=93358"}],"version-history":[{"count":1,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/93358\/revisions"}],"predecessor-version":[{"id":93360,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/93358\/revisions\/93360"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/media\/93359"}],"wp:attachment":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=93358"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=93358"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=93358"},{"taxonomy":"location","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Flocation&post=93358"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}