MathDB

x^3, y^3 , x + y are rational, then xy, x^2+y^2, x, y are also rational

Source: Norwegian Mathematical Olympiad 2001 - Abel Competition p1b

February 22, 2020

rationalalgebra

Problem Statement

Suppose that

x

and

y

are positive real numbers such that

x^3, y^3

and

x + y

are all rational numbers. Show that the numbers

xy, x^2+y^2, x

and

y

are also rational