Math olympiad problem

Question

Let a and b be positive whole integers, for which a^2 - b^2 is a power of two. Prove that a^2 + b^2 is the sum of two powers of two (powers of two are 2^0, 2^1, 2^2 …

Answer 1

hint: what can a+b and a-b be?

Answer 2

a² - b² = (a+b)(a-b). Since a and b are integers, those two terms are also powers of two. (a-b)² + (a+b)² = 2a²+2b² is a sum of two powers of 2