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?
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?
yes, but just because 2xy is an integer, it doesn't say anything about x, y, or xy.
thats where im stumped