On the sequence
Alexandr Grebennikov
Saint-Petersburg State University, Russia; IMPA, Rio de Janeiro, BrazilArsenii Sagdeev
Alfréd Rényi Institute of Mathematics, Budapest, HungaryAliaksei Semchankau
Moscow State University; Saint-Petersburg State University, RussiaAliaksei Vasilevskii
Carnegie Mellon University, Pittsburgh, USA
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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. 40 (2024), no. 2, pp. 637–648
DOI 10.4171/RMI/1422