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An easy 3 variable equation

Source: Turkey National Mathematical Olympiad 2022 P4

December 23, 2022
Diophantine equationnumber theory

Problem Statement

For which real numbers aa, there exist pairwise different real numbers x,y,zx, y, z satisfying x3+ay+z=y3+ax+z=z3+ax+y=−3.\frac{x^3+a}{y+z}=\frac{y^3+a}{x+z}=\frac{z^3+a}{x+y}= -3.
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