An incomplete variant of Wilson's congruence

Joel Beeren; David Harvey; Tim Trudgian

An incomplete variant of Wilson's congruence

Number Theory 2013-10-11 v1

Authors: Joel Beeren , David Harvey , Tim Trudgian

Abstract

This article examines the nontrivial solutions of the congruence $(p-1)\cdots(p-r) \equiv -1 \pmod p.$ We discuss heuristics for the proportion of primes $p$ that have exactly $N$ solutions to this congruence. We supply numerical evidence in favour of these conjectures, and discuss the algorithms used in our calculations.

Keywords

wilson's congruence prime numbers modular arithmetic nontrivial solutions number theory heuristics algorithms

Cite

@article{arxiv.1310.2691,
  title  = {An incomplete variant of Wilson's congruence},
  author = {Joel Beeren and David Harvey and Tim Trudgian},
  journal= {arXiv preprint arXiv:1310.2691},
  year   = {2013}
}

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7 pages, 2 tables

An incomplete variant of Wilson's congruence

Abstract

Keywords

Cite

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