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Point with integer coordinates

Source: Italy, 1986

July 17, 2006
analytic geometrygraphing linesslope

Problem Statement

Prove that a circle centered at point (2,3)(\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)(0,0) has at most one point with coordinates (a−2,b−3)(a-\sqrt{2},b-\sqrt{3});a,b∈Za,b \in \mathbb{Z}. So that when we translate the center to (2,3)(\sqrt{2},\sqrt{3}) we have what we wanted to show.
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