A. Edery

Summing the reciprocal of the polynomial appearing in Fermat's Last Theorem

Consider the polynomial $f=x^N+y^N-z^N$ where $x,\,y$ and $z$ are positive integers and $N \ge 3$ is an integer. By Fermat's Last Theorem, $f$ is never zero so that its reciprocal, $1/f$, has no singularities. We therefore study the finite sum of the reciprocal: $S(m,N)=\sum_{x=1}^m\sum_{y=1}^m\sum_{z=1}^{m}\frac{1}{f}...