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find n such that x^n+y^n+z^n is constant for all x,y,z x+y+z=0 and xyz=1.

Source: 2009 Belarus TST 1.2

November 8, 2020

algebraconstantexponential

Problem Statement

Find all

n \in N

for which the value of the expression

x^n+y^n+z^n

is constant for all

x,y,z \in R

such that

x+y+z=0

and

xyz=1

.
D. Bazylev