{"id":976,"date":"2021-12-18T11:07:47","date_gmt":"2021-12-18T11:07:47","guid":{"rendered":"https:\/\/adrianbell.me\/?p=976"},"modified":"2021-12-18T11:07:49","modified_gmt":"2021-12-18T11:07:49","slug":"chapter-9-of-24-multiplicative-functions","status":"publish","type":"post","link":"http:\/\/adrianbell.me\/?p=976","title":{"rendered":"Chapter 9 of 24 - Multiplicative Functions"},"content":{"rendered":"\n

Multiplication! That sounds nice and simple doesn't it! Unfortunately, that's not what that title means. <\/p>\n\n\n\n

Any number can be broken down into its prime decomposition (\"15=3\times 5\"). A multiplicative function is where a function of a number is equal to the function of each prime in the prime decomposition of that number all multiplied together. So if \"n=p_1\times p_2\", where p is a prime in the prime decomposition and if \"f(n) = f(p_{1}\times p_{2}) = f(p_{1})\times f(p_{2})\", then the function \"f\" is a multiplicative function. <\/p>\n\n\n\n

Next section went into detail about perfect numbers. A perfect number is equal to the sum of its positive factors excluding itself. Best example here is the perfect number 6=1+2+3.<\/p>\n\n\n\n

The rest of the chapter was introducing Euler's \"\phi\"-function (also multiplicative), and using this new function, the introduction of primitive roots. <\/p>\n","protected":false},"excerpt":{"rendered":"

Multiplication! That sounds nice and simple doesn't it! Unfortunately, that's not what that title means. Any number can be broken down into its prime decomposition (). A multiplicative function is where a function of a number is equal to the function of each prime in the prime decomposition of that number all multiplied together. So … Continue reading Chapter 9 of 24 - Multiplicative Functions<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[32],"tags":[45],"class_list":["post-976","post","type-post","status-publish","format-standard","hentry","category-pure-maths","tag-pure-maths"],"_links":{"self":[{"href":"http:\/\/adrianbell.me\/index.php?rest_route=\/wp\/v2\/posts\/976","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/adrianbell.me\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/adrianbell.me\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/adrianbell.me\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/adrianbell.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=976"}],"version-history":[{"count":5,"href":"http:\/\/adrianbell.me\/index.php?rest_route=\/wp\/v2\/posts\/976\/revisions"}],"predecessor-version":[{"id":981,"href":"http:\/\/adrianbell.me\/index.php?rest_route=\/wp\/v2\/posts\/976\/revisions\/981"}],"wp:attachment":[{"href":"http:\/\/adrianbell.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=976"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/adrianbell.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=976"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/adrianbell.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}