We prove that the sequence produces at least distinct residues modulo prime . Moreover, the factorials within an interval of length produce at least distinct residues modulo . As a corollary, we prove that every non-zero residue class can be expressed as a product of seven factorials modulo , where for all , which provides a polynomial improvement upon the preceding results.
Cite this article
Alexandr Grebennikov, Arsenii Sagdeev, Aliaksei Semchankau, Aliaksei Vasilevskii, On the sequence . Rev. Mat. Iberoam. (2023), published online firstDOI 10.4171/RMI/1422