Definition

$\varphi (n)$ is the number of integers between 0 and n-1 who is coprime with n. $\varphi (n):=|a:0⩽a<n\wedge (a,n)=1|$

Properties

1. Let a be an integer comprime with n. Then $a^{\mathrm{\Phi }(n)}\equiv 1modn$
2. (m,n)=1 $⟹\varphi (mn)=\varphi (m)\cdot \varphi (n)$
3. $\sum _{d\mid n}\mathrm{\Phi }(d)=n$