VN-TST 2009 Problem 3

Let a, b be positive integers. a, b and a.b are not perfect squares.

Prove that at most one of following equations

$ax^2 - by^2 = 1$ and $ax^2 - by^2 = - 1$

has solutions in positive integers.

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.