On the sequence $n!\mathrm{mod}p$

A. Grebennikov, A. Sagdeev, A. Semchankau +1

We prove, that the sequence $1!,2!,3!,\dots$ produces at least $(\sqrt{2}+o(1))\sqrt{p}$ distinct residues modulo prime $p$. Moreover, factorials on an interval $\mathcal{I} \…