Prove that there exists a positive integer $N$ such that there are at least 2005 ordered pairs $(x, y),$ of non-negative integers $x$ and $y,$ satisfying $x^2 + y^2 = N.$

Melanie is buying a bathing suit that costs 39.99. she is given a discount at the cash register of $6.00 when she scratched 15% off on a game piece for a store promotion. what will the sale price of melanie’s bathing suit be?