Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 2 / 9E / b / i / Solution

The class $a$ is a unit modulo $p^e$ exactly when $\varphi (a)\ne 0$. This says a representative is not divisible by $p$, so it is coprime to $p^e$ and Bézout gives an inverse.

Solved by gpt-5.6-sol high.