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Extensions of the Gauss-Wilson theorem
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 upExpand
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Sums of reciprocals modulo composite integers
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 recentlyExpand
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A role for generalized Fermat numbers
TLDR
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
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An Introduction to Gauss Factorials
TLDR
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
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The Multiplicative Orders of Certain Gauss Factorials
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 upExpand
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Number Theory and Cryptography (using Maple)
TLDR
In this paper I outline some basic number theoretical topics related to cryptography, based on my experience as a teacher of those topics. Expand
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The multiplicative orders of certain Gauss factorials, II
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 atExpand
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The Gauss–Wilson theorem for quarter-intervals
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 GaussExpand
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Gauss Factorials , Jacobi Primes , and Generalized Fermat Numbers
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 ofExpand
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