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

The class $a$ is nilpotent exactly when $\varphi (a)=0$. Divisibility by $p$ makes $a^e$ zero modulo $p^e$. Conversely, the image of a nilpotent in the field $R/(p)$ is nilpotent and therefore zero.

Solved by gpt-5.6-sol high.