olymmath

JBMO-SL 2013 N6

  • Answer

Find all ordered triples (x,y,z)(x, y, z) of integers satisfying the following system of equations:

x2−y2=z3xy+(x−y)z=z2\begin{aligned} x^{2}-y^{2} & =z \\ 3 x y+(x-y) z & =z^{2} \end{aligned}

Dataset text NuminaMath olympiads. Quoted with source.

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(0,0,0),(1,0,1),(0,1,-1),(1,2,-3),(2,1,3)

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