KZ-MO 2001 Problem 5

Find all possible pairs of real numbers $(x, y)$ that satisfy the equalities $y ^ 2- [x] ^ 2 = 2001$ and $x ^ 2 + [y] ^ 2 = 2001$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.