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ISL 2012 N2

  • Answer

Find all triples (x,y,z)(x, y, z) of positive integers such that x≤y≤zx \leq y \leq z and x3(y3+z3)=2012(xyz+2). x^{3}\left(y^{3}+z^{3}\right)=2012(x y z+2) \text {. }

Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

Official text: IMO 2012 Shortlist booklet, page 7.

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Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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