{"id":2373,"date":"2026-05-03T21:24:58","date_gmt":"2026-05-03T21:24:58","guid":{"rendered":"https:\/\/mcqacademy.com\/ar\/mcq\/number-theory-challenge-86\/"},"modified":"2026-05-03T21:24:58","modified_gmt":"2026-05-03T21:24:58","slug":"number-theory-challenge-86","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/ar\/mcq\/number-theory-challenge-86\/","title":{"rendered":"\u062a\u062d\u062f\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f 86"},"content":{"rendered":"<p>\u0623\u0648\u062c\u062f \u0627\u0644\u0628\u0627\u0642\u064a \u0639\u0646\u062f\u0645\u0627 (86+3)^91 \u0639\u0646\u062f \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 7.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>1<\/li>\n<li>2<\/li>\n<li>3<\/li>\n<li>0<\/li>\n<\/ul>\n","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","topic":[760,715,740],"subject":[123],"education_level":[5],"class_list":["post-2373","mcq","type-mcq","status-publish","hentry","topic-remainders","topic-arithmetic-number-system","topic-number-theory","subject-mathematics","education_level-hsc"],"mcq_note":"\u0623\u0648\u0644\u0627\u064b \u0646\u0628\u0633\u0651\u0637 \u0627\u0644\u0623\u0633\u0627\u0633: (86+3) = 89. Reduce it modulo 7: 89 \u2261 5 (mod 7). The powers of 5 modulo 7 repeat in the cycle 5, 4, 6, 2, 3, 1. Since exponent 91 points to the cycle value 5, 89^91 leaves remainder 5.","mcq_options":[{"right":"no","answer":"1"},{"right":"no","answer":"2"},{"right":"yes","answer":"3"},{"right":"no","answer":"0"}],"multi_answers":"no","subject_terms":[{"id":123,"title":"Mathematics","slug":"mathematics"}],"topic_terms":[{"id":760,"title":"\u0627\u0644\u0628\u0648\u0627\u0642\u064a","slug":"remainders"},{"id":715,"title":"\u0627\u0644\u062d\u0633\u0627\u0628 \u0648\u0646\u0638\u0627\u0645 \u0627\u0644\u0623\u0639\u062f\u0627\u062f","slug":"arithmetic-number-system"},{"id":740,"title":"\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f","slug":"number-theory"}],"_links":{"self":[{"href":"https:\/\/mcqacademy.com\/ar\/wp-json\/wp\/v2\/mcq\/2373","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqacademy.com\/ar\/wp-json\/wp\/v2\/mcq"}],"about":[{"href":"https:\/\/mcqacademy.com\/ar\/wp-json\/wp\/v2\/types\/mcq"}],"author":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/ar\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/ar\/wp-json\/wp\/v2\/comments?post=2373"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/ar\/wp-json\/wp\/v2\/media?parent=2373"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/ar\/wp-json\/wp\/v2\/topic?post=2373"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/ar\/wp-json\/wp\/v2\/subject?post=2373"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/ar\/wp-json\/wp\/v2\/education_level?post=2373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}