51st Ukrainian National Mathematical Olympiad, 3rd Round

Question

Prove that there exists infinitely many squares that can be represented as 2^n + 2^m, where n, m are distinct natural numbers.

Accepted Answer

Let n = m + 3, then N = 2^n + 2^m = 2^m(2^3 + 1) = 2^m 9, and we can take m = 2s.