A theorem of Gauss extending Wilson’s theorem states the congruence (n − 1)n! ≡ −1 (mod n) whenever n has a primitive root, and ≡ 1 (mod n) otherwise, where Nn! denotes the product of all integers up… Expand

In 1938, as part of a wider study, Emma Lehmer derived a set of four related congruences for certain sums of reciprocals over various ranges, modulo squares of odd primes. These were recently… Expand

We study particular aspects of the Gauss factorials bn−1 M cn! for M = 3 and 6, where the case of n having exactly one prime factor of the form p ≡ 1 (mod 6) is of particular interest.Expand

We present results on Gauss factorials , and more generally on partial products obtained when the product (n - 1)n! is divided into M equal parts, for integers M ≥ 2.Expand

A theorem of Gauss extending Wilson's theorem states the congruence (n - 1)n! ≡ -1 (mod n) whenever n has a primitive root, and ≡ 1 (mod n) otherwise, where Nn! denotes the product of all integers up… Expand

2. There are numerous items that can be studied in number theory, and as mentioned above the authors have not made a sufficient case for another 20 page paper by themselves in this field. Looking at… Expand

We define a Gauss factorial Nn! to be the product of all positive integers up to N that are relatively prime to n. It is the purpose of this paper to study the multiplicative orders of the Gauss… Expand

Given positive integers N andn, we define the Gauss factorial Nn! as the product of all positive integers from 1 to N and coprime to n. In this expository paper we begin with the classical theorem of… Expand