Remarks on an interpolation between Wilson's theorem and Giuga's conjecture

TL;DR

This paper introduces a family of congruences that bridge Wilson's theorem and Giuga's conjecture, providing elementary results to explore a potential approach to prove Giuga's conjecture.

Contribution

It constructs a new family of congruences linking Wilson's theorem and Giuga's conjecture, offering a novel framework for investigation.

Findings

Elementary results on the interpolating congruences

A potential approach to Giuga's conjecture

New insights into the relationship between Wilson's theorem and Giuga's conjecture

Abstract

A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.