On the sequence

  • Alexandr Grebennikov

    Saint-Petersburg State University, Russia; IMPA, Rio de Janeiro, Brazil
  • Arsenii Sagdeev

    Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Aliaksei Semchankau

    Moscow State University; Saint-Petersburg State University, Russia
  • Aliaksei Vasilevskii

    Carnegie Mellon University, Pittsburgh, USA
On the sequence $n! \bmod p$ cover
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Abstract

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 first

DOI 10.4171/RMI/1422