Problem

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Tags: AMC, USA(J)MO, USAJMO, conics, parabola, analytic geometry, nt



A triangle is called a parabolic triangle if its vertices lie on a parabola $y = x^2$. Prove that for every nonnegative integer $n$, there is an odd number $m$ and a parabolic triangle with vertices at three distinct points with integer coordinates with area $(2^nm)^2$.