What is the summation notation of: $f(x,y,z)=\dfrac{(x+y+z)^n-(x^n+y^n+z^n)}{ (x+y)(y+z) (z+x)}$?

Question

Let $x,y,z$ be integers where $(x+y)(y+z) (z+x)\neq 0$ and $ n$ is odd prime. Find the summation notation of: $$f(x,y,z)=\dfrac{(x+y+z)^n-(x^n+y^n+z^n)}{ (x+y)(y+z) (z+x)}$$ Any hints?

Answer 1

This function is examined in detail in Ribenboim’s Fermat’s Last Theorem for Amateurs, Chapter VII.