{"id":2503,"date":"2021-12-18T08:01:42","date_gmt":"2021-12-18T13:01:42","guid":{"rendered":"https:\/\/josmfs.net\/?p=2503"},"modified":"2024-04-06T17:26:04","modified_gmt":"2024-04-06T21:26:04","slug":"remainder-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/12\/18\/remainder-problem\/","title":{"rendered":"Remainder Problem"},"content":{"rendered":"

\"\"Here is a challenging problem from the 2021 Math Calendar.<\/p>\n

\u201cFind the remainder from dividing the polynomial<\/p>\n

x<\/em>20<\/sup> + x<\/em>15<\/sup> + x<\/em>10<\/sup> + x<\/em>5<\/sup> + x<\/em> + 1<\/p>\n

by the polynomial<\/p>\n

x<\/em>4<\/sup> + x<\/em>3<\/sup> + x<\/em>2<\/sup> + x<\/em> + 1\u201d<\/p>\n

Recall that all the answers are integer days of the month.<\/p>\n

Answer<\/a>.<\/p>\n

See the Remainder Problem<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here is a challenging problem from the 2021 Math Calendar. \u201cFind the remainder from dividing the polynomial x20 + x15 + x10 + x5 + x + 1 by the polynomial x4 + x3 + x2 + x + 1\u201d Recall that all the answers are integer days of the month. Answer. See the Remainder […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[133,183],"class_list":["post-2503","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-algebra","tag-math-calendar"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2503"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2503\/revisions"}],"predecessor-version":[{"id":3654,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2503\/revisions\/3654"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}