Let $\frac{x^2}{a^2}-\frac{y^2}{b^2} = 1$the hyperbola be canonical.
Find all integer points of the plane that belong to the hyperbola.
My idea:
We can multiply by $(ab)^2$, then it can be rewritten as $(bx-ay)(bx+ay) = (ab)^2$, But this argument does not give much, if $a,b$ not integers, but real. Otherwise, it would be possible to compile a system for each factorization.
Thanks in advance for any help.