Products of factorials modulo $p$
Volume 96 / 2003
Colloquium Mathematicum 96 (2003), 191-205
MSC: 11A07, 11N69, 11B65.
DOI: 10.4064/cm96-2-4
Abstract
We show that if $p\ne 5$ is a prime, then the numbers $$ \left\{{1 \over p} \left({p\atop {m_1,\dots,m_t}}\right) \biggm| t\ge 1,\, m_i\ge 0\ \hbox{for}\ i=1,\dots,t \ \hbox{and}~\sum_{i=1}^t m_i=p\right\} $$ cover all the nonzero residue classes modulo $p$.
