Show that every square is congruent to 0,1 or -1 modulo 5 , and is congruent to 0,1 or 4 modulo 8 .

Suppose \(n\) is a positive integer such that both \(2 n+1\) and \(3 n+1\) are squares. Prove that \(n\) is divisible by 40 .

Find a value of \(n\) such that \(2 n+1\) and \(3 n+1\) are squares. Can you find another value? (Calculators allowed!)