Let $m$ and $n$ be two integers such that $(m, n) = 1$ and $\phi(m) =\phi(n) $. Then there exists a single residue system which is congruent both modulo $m$ as well as $n$.
What i know is that if $(m, n) = 1$, then $$(m, 2m, \cdots, nm)$$ forms a complete residue system modulo $n$. How to use this fact?