Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 4 / 6E / d / Solution

The class of $(1,1)$ isso its size is Euler's totient functionThe unit group acts freely on every pair in $Y$: if $\lambda a\equiv a$ and $\lambda b\equiv b$, multiplying the Bezout identity by $\lambda -1$ gives $\lambda \equiv 1(\mathrm{mod}n)$. Hence every equivalence class has size $\phi (n)$. Dividing the answer from part (a) by this size gives