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x + y -z = 6 , x^3 + y^3 -z^3 = 414, diophantine

Source: 2020 Chile National Olympiad level 2 p4

October 22, 2022
number theoryDiophantine equationDiophantine Equationsdiophantinesystem of equations

Problem Statement

Determine all three integers (x,y,z)(x, y, z) that are solutions of the system x+y−z=6x + y -z = 6 x3+y3−z3=414x^3 + y^3 -z^3 = 414
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