Lucas's Theorem

The primitive factors $Q_n(x,y)$ of $x^n+y^n$ can be written in the form

$$Q_n(x,y)=U^2(x,y)\pm nxyV^2(x,y)$$

for Squarefree $n$ where $U$ and $V$ are Homogeneous Polynomials with the sign chosen according to

$$\cases{ + & for $n=4l+1$\cr - & for $n=4l+3$\cr {\rm either} & for $n=4l+2$.\cr}$$