Question 3
Let $a,b$ be positive integers such that none of $a,b,ab$ is a perfect square. Prove that at least one of the equations
$$ax^2-by^2=1,\qquad ax^2-by^2=-1$$
has no solution in positive integers.
$$ax^2-by^2=1,\qquad ax^2-by^2=-1$$
has no solution in positive integers.