Sets whose differences avoid squares modulo m

Abstract

We prove that if $\epsilon (m)\to 0$ arbitrarily slowly, then for almost all $m$ and any $A\subset {\mathbb{Z}}_m$ such that $A-A$ does not contain non-zero quadratic residues we have $|A|\le m^{1/2-\epsilon (m)}.$

14 pages

References in corpus (1)

• Joint Poisson distribution of prime factors in sets