I need to prove the proposition.
Let $a$ be an arbitrary integer. Then for every positive integer $n$, we have $$\sum_{d \mid n}\phi\left(\frac{n}{d}\right)a^d\equiv0\pmod{n}.$$
I need to prove the proposition.
Let $a$ be an arbitrary integer. Then for every positive integer $n$, we have $$\sum_{d \mid n}\phi\left(\frac{n}{d}\right)a^d\equiv0\pmod{n}.$$