Euler Theorem

by {"name"=>"Yuan Lu", "avatar"=>"me.jpg", "bio"=>"Working on blockchain, cryptography, and DApps.", "location"=>"Beijing, China", "employer"=>nil, "pubmed"=>nil, "googlescholar"=>"https://scholar.google.com/citations?user=T0_K2P0AAAAJ", "email"=>"luyuan@iscas.ac.cn", "researchgate"=>nil, "uri"=>nil, "bitbucket"=>nil, "codepen"=>nil, "dribbble"=>nil, "flickr"=>nil, "facebook"=>nil, "foursquare"=>nil, "github"=>"yylluu", "google_plus"=>nil, "keybase"=>nil, "instagram"=>nil, "lastfm"=>nil, "linkedin"=>"lu-yuan", "orcid"=>nil, "pinterest"=>nil, "soundcloud"=>nil, "stackoverflow"=>nil, "steam"=>nil, "tumblr"=>nil, "twitter"=>nil, "vine"=>nil, "weibo"=>nil, "xing"=>nil, "youtube"=>nil, "wikipedia"=>nil}

$ gcd(a,n)=1 \Rightarrow a^{\varphi(n)} \equiv 1 \mod n$

Preliminary: Euler’s totient function

Defining $\varphi(n)$

Statement

Prove