olymmath

JBMO-SL 2013 N5

  • Answer

Find all ordered triples (x,y,z)(x, y, z) of positive integers satisfying the equation

1x2+yxz+1z2=12013\frac{1}{x^{2}}+\frac{y}{x z}+\frac{1}{z^{2}}=\frac{1}{2013}

Dataset text NuminaMath olympiads. Quoted with source.

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(x, y, z)=\left(2013 n, 2013 n^{2}-2,2013 n\right)

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