Equal sums of like polynomials

Abstract

Let $f$ be a polynomial of degree $d>6$, with integer coefficients. Then the paucity of non-trivial positive integer solutions to the equation $f(a)+f(b)=f(c)+f(d)$ is established. The corresponding situation for equal sums of three like polynomials is also investigated.

8 pages; to appear in Bull. London Math. Soc