Question 2
1. Prove that there are infinitely many positive integers $t$ such that $2012t+1$ and $2013t+1$ are both perfect squares.
2. Let $m,n$ be positive integers such that $mn+1$ and $(m+1)n+1$ are both perfect squares. Prove that $8(2m+1)$ divides $n$.
2. Let $m,n$ be positive integers such that $mn+1$ and $(m+1)n+1$ are both perfect squares. Prove that $8(2m+1)$ divides $n$.