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algebra problem

Source: Bundeswettbewerb Mathematik 2023 Round 1 P2

March 9, 2023
bundeswettbewerbalgebramath competition

Problem Statement

Determine all triples (x,y,z)(x, y, z) of integers that satisfy the equation x2+y2+z2−xy−yz−zx=3x^2+ y^2+ z^2 - xy - yz - zx = 3
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