If \(x+y\), \(x^2+y^2\), \(x^3+y^3\), and \(x^4+y^4\) are all integers, and \(x\) and \(y \) are both real numbers, do \(x\) and \(y\) have to be integers as well?

AvenJohn Feb 20, 2022

#1**+1 **

I think so.

Here is my reasoning: \(x^2+y^2= (x+y)^2-2xy\), since we know x+y is an integer, and x^2+y^2 is also an integer, then -2xy must be an integer.

maybe someone else can do this as well?

Guest Feb 20, 2022