Question

Prove that either 2 · 10500 + 15 or 2 · 10500 + 16 is not a perfect square. is your proof constructive or nonconstructive?

Answer 1

A perfect square is a square of an integer. 

Proof. 0 and 1 are the only two perfect squares that differ by 1. Any other numbers differ by 1 cannot both be perfect squares. Non-perfect square must exist in any set that contains two numbers that differ by 1. 

We used non-constructive proof. We indirectly showed that proof exists without providing an example.