MathDB

x^n+y^n in Z for n in [4], then n=5 holds for complex x,y

Source: VJIMC 1999 1.4

August 1, 2021

algebranumber theorycomplex numbers

Problem Statement

Show that the following implication holds for any two complex numbers

x

and

y

: if

x+y

x^2+y^2

x^3+y^3

x^4+y^4\in\mathbb Z

, then

x^n+y^n\in\mathbb Z

for all natural n.