INMO 2000 Problem 2

Solve for integers $x, y, z$ :

$x+y=1-z, x^{3}+y^{3}=1-z^{2}$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

(m, -m, 1), (0, 1, 0), (-2, -3, 6), (1, 0, 0), (0, -2, 3), (-2, 0, 3), (-3, -2, 6)

Solutions

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