Proof of the Kakeya set conjecture over rings of integers modulo square-free $N$

Manik Dhar, Zeev Dvir

A Kakeya set $S\subset (\mathbb{Z}/N\mathbb{Z}{)}^n$ is a set containing a line in each direction. We show that, when $N$ is any square-free integer, the size of the smallest Kakeya…