Powerful SquaresNumber Theory Level 5
Let \((m, n)\) be an ordered pair of positive integers such that \(5^m - 7^n\) is a perfect square. Find the maximum possible value of \(m + n\).
If you think there is no maximum value, i.e. there are infinitely many pairs \((m, n)\) that satisfy the condition, input \(-1\) as your answer.
Note: A perfect square must be nonnegative.