# Carmichael Function

the exponent of the multiplicative group of integers modulo $n$ is $\lambda(n)$

## 性質

$n = p_1^{r_1} p_2^{r_2} \cdots p_k^{r_k}$

$\lambda(n) = lcm(\lambda(p_1^{r_1}),\lambda(p_2^{r_2}), \cdots, \lambda(p_k^{r_k}))$

$p$ 是質數，$\lambda(p^k) = {\begin{cases}\frac{\varphi(p^k)}{2}& p = 2, k > 2\\\varphi(p^k)& else \end{cases}}$$\varphi$Euler's Totient Function