English

A solution to a Paul Erdos problem

Number Theory 2025-05-09 v3 Combinatorics

Abstract

Paul Erdos posed the following question: Is there a prime number p>5p>5 such that the residues of 2!2!, 3!3!,\ldots, (p1)!(p-1)! modulo pp all are distinct? In this short note, we prove that there are no such prime numbers.

Keywords

Cite

@article{arxiv.2504.19392,
  title  = {A solution to a Paul Erdos problem},
  author = {Vyacheslav M. Abramov},
  journal= {arXiv preprint arXiv:2504.19392},
  year   = {2025}
}

Comments

Dear readers, I need to withdraw this paper since I was shown a counterexample. At this moment I cannot fix an error. I shall return to this question as soon as I find a solution

R2 v1 2026-06-28T23:13:08.773Z