English

On distinct residues of factorials

Number Theory 2018-05-22 v1

Abstract

We investigate the existence of primes p>5p > 5 for which the residues of 2!2!, 3!3!, \dots, (p1)!(p-1)! modulo pp are all distinct. We describe the connection between this problem and Kurepa's left factorial function, and report that there are no such primes less than 101110^{11}.

Keywords

Cite

@article{arxiv.1603.04086,
  title  = {On distinct residues of factorials},
  author = {Vladica Andrejić and Milos Tatarevic},
  journal= {arXiv preprint arXiv:1603.04086},
  year   = {2018}
}