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

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.   

1) angle MPN = angle MNT | Given

2) angle PMN = angle PMN | Common angles

Step-by-step explanation:

Therefore, by the AA theorem of similarity angle PMN = angle NMT