Question 59
1. Prove that there exists infinitely many positive integer $t$ such that $t$ both $2012t+1$ and $2013t+1$ are perfect square.
2. Let $m, n$ be positive integers such that both $mn+1$ and $(m+1)n+1$ are perfect square. Prove that $n$ is divisible by $8(2m+1)$.
2. Let $m, n$ be positive integers such that both $mn+1$ and $(m+1)n+1$ are perfect square. Prove that $n$ is divisible by $8(2m+1)$.