OSN 2009 Problem 7

A pair of integers $(m,n)$ is called good if $$m\mid n^2 + n \ \text{and} \ n\mid m^2 + m$$ Given 2 positive integers $a,b > 1$ which are relatively prime, prove that there exists a good pair $(m,n)$ with $a\mid m$ and $b\mid n$ , but $a\nmid n$ and $b\nmid m$ .