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Proof WritingMediumPigeonhole and Extremal Arguments

Pigeonhole and Extremal Arguments · Medium problem

How many integer triples (x,y,z)(x, y, z) with ∣x∣,∣y∣,∣z∣≤20|x|, |y|, |z| \le 20 satisfy x2+y2=3z2x^2 + y^2 = 3z^2?