IMO 2016 Shortlist N5
Let a be a positive integer which is not a square number. Denote by A the set of all positive integers k such that k = x...
Category: Number Theory
Problem
Let a be a positive integer which is not a square number. Denote by A the set of all positive integers k such that k = x2 − a x2 − y2 (1) for some integers x and y with x > √ a. Denote by B the set of all positive integers k such that (1) is satisfied for some integers x and y with 0 ⩽ x < √ a. Prove that A = B.