IT-CESENATICO 1986 Problem 4

Prove that a circle centered at point $(\sqrt{2},\sqrt{3})$ in the cartesian plane passes through at most one point with integer coordinates.

I tried to prove that any circle with center at $(0,0)$ has at most one point with coordinates $(a-\sqrt{2},b-\sqrt{3})$ ; $a,b \in \mathbb{Z}$ . So that when we translate the center to $(\sqrt{2},\sqrt{3})$ we have what we wanted to show.