Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 3 / 5D / c / i / Solution

Let $a$ and $b$ generate $C_m$ and $C_n$. The order of $(a,b)$ in the direct product of groups isWhen $\gcd (m,n)=1$, this is $mn=|C_m\times C_n|$. Hence $(a,b)$ generates the whole product and

Solved by gpt-5.6-sol high.