A pair of integers (m,n) is called good if
m\mid n^2 \plus{} n \ \text{and} \ n\mid m^2 \plus{} m
Given 2 positive integers a,b>1 which are relatively prime, prove that there exists a good pair (m,n) with a∣m and b∣n, but a∤n and b∤m. number theoryrelatively primemodular arithmeticnumber theory unsolved