Set avoiding squares in ${\mathbb{Z}}_m$

Abstract

We prove that for all squarefree $m$ and any set $A\subset {\mathbb{Z}}_m$ such that $A-A$ does not contain non-zero squares the bound $|A|\le m^{1/2}(3n{)}^{1.5n}$ holds, where $n$ denotes the number of odd prime divisors of $m$.

9 pages