{"id":166413,"date":"2024-04-05T15:01:02","date_gmt":"2024-04-05T09:31:02","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=166413"},"modified":"2024-04-05T15:01:03","modified_gmt":"2024-04-05T09:31:03","slug":"how-many-pairs-of-positive-integersof-mn-satisfy-the-equation-m%c2%b2-105-n%c2%b2","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/how-many-pairs-of-positive-integersof-mn-satisfy-the-equation-m%c2%b2-105-n%c2%b2\/","title":{"rendered":"How many pairs of positive integers(of m,n) satisfy the equation m\u00b2 + 105 = n\u00b2"},"content":{"rendered":"\n<p>How many pairs of positive integers(of m,n) satisfy the equation m\u00b2 + 105 = n\u00b2<\/p>\n\n\n\n<p>a)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2<\/p>\n\n\n\n<p><strong>b)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 3<\/strong><\/p>\n\n\n\n<p>c)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4<\/p>\n\n\n\n<p>d)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 5<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>m\u00b2 \u2013 n\u00b2 = 105<\/p>\n\n\n\n<p>(m \u2013 n) (n + m) = 105<\/p>\n\n\n\n<p>105 = 3 \u00d7 35 \u21d2 m = 19, n = 16<\/p>\n\n\n\n<p>105 = 5 \u00d7 21 \u21d2 m = 13, n = 8<\/p>\n\n\n\n<p>105 = 7 \u00d7 15 \u21d2 m = 11, n = 4<\/p>\n\n\n\n<p>\u21d2 3 pairs of (m, n)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How many pairs of positive integers(of m,n) satisfy the equation m\u00b2 + 105 = n\u00b2 a)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2 b)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 3 c)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4 d)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 5 Sol: m\u00b2 \u2013 n\u00b2 = 105 (m \u2013 n) (n + m) = 105 105 = 3 \u00d7 35 \u21d2 m = 19, n = 16 105 = 5 \u00d7 21 \u21d2 [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":166414,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5138],"tags":[5139],"offerexpiration":[],"class_list":["post-166413","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantitative-aptitude","tag-quantitative-aptitude"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/166413","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=166413"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/166413\/revisions"}],"predecessor-version":[{"id":166415,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/166413\/revisions\/166415"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/166414"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=166413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=166413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=166413"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/offerexpiration?post=166413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}