Generalised Fermat equations in dense variables over finite fields and rings

by @math-papers

Abstract. Let $A$ be a sufficiently dense subset of a finite field ${\mathbb{F}} {q}$ or a finite, cyclic ring ${{\mathbb{Z}}/N}\hspace{0pt}{\mathbb{Z}}$. Assuming that $q$ and $N$ have no small prime divisors, we show t…