olymmath

BALTIC-WAY 1994 Problem 1

  • Answer

Let a∘b=a+b−aba \circ b=a+b-a b. Find all triples (x,y,z)(x, y, z) of integers such that (x∘y)∘z+(y∘z)∘x+(z∘x)∘y=0(x \circ y) \circ z+(y \circ z) \circ x+(z \circ x) \circ y=0.

Dataset text NuminaMath olympiads. Quoted with source.

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(0,0,0), (0,2,2), (2,0,2), (2,2,0)

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