MathDB

x^n+y^n+z^n is constant

Source: Spanish Mathematical Olympiad 2013. Problem 2

March 26, 2015

algebra

Problem Statement

Find all the possible values of a positive integer

n

for which the expression

S_n=x^n+y^n+z^n

is constant for all real

x,y,z

with

xyz=1

and

x+y+z=0