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BALKAN-SL 2016 N3

  • Answer

Find all the integer solutions (x,y,z)(x, y, z) of the equation

(x+y+z)5=80xyz(x2+y2+z2)(x+y+z)^{5}=80 x y z\left(x^{2}+y^{2}+z^{2}\right)

Dataset text NuminaMath olympiads. Quoted with source.

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(x, y, z) \in{(0, t,-t),(t, 0,-t),(t,-t, 0): t \in \mathbb{Z}}

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