# Euler's Totient Function

the order of the multiplicative group of integers modulo $n$ is $\varphi(n)$

## 性質

$gcd(m, n) = 1$$\varphi(mn) = \varphi(m) \varphi(n)$

$p$ 是質數，$\varphi(p) = p - 1$

$p$ 是質數，$\varphi(p^k) = p ^ {k - 1}(p - 1) = p ^ k (1 - \frac{1}{p})$