Solution
= Solution
The class $a$ is a unit modulo $p^e$ exactly when $\phi(a)\ne0$. This says a representative is not divisible by $p$, so it is coprime to $p^e$ and Bézout gives an inverse.
= Solution
The class $a$ is a unit modulo $p^e$ exactly when $\phi(a)\ne0$. This says a representative is not divisible by $p$, so it is coprime to $p^e$ and Bézout gives an inverse.