Variations on a result of Granville about polynomial invariance

Abstract

In 2004, Andrew Granville proved the following: A polynomial in variables $x,y,z,$ invariant under the map $\phi :z\to -(x+y+z)$ is a polynomial in $b=z(x+y+z)$. We tell, curtly, its history and then give a variation on this theme.

9 pages