Gauss Factorials: Properties and Applications

Abstract

Starting with Wilson's theorem and its generalization by Gauss, we define a Gauss factorial TeX Embedding failed! to be the product of all positive integers up to TeX Embedding failed! and relatively prime to TeX Embedding failed!. We present results on the Gauss factorials TeX Embedding failed!, and more generally on partial products obtained when the product TeX Embedding failed! is divided into TeX Embedding failed! equal parts, for integers TeX Embedding failed!. Finally, extensions of the Gauss binomial coefficient theorem are presented in terms of Gauss factorials. (Joint work with John B. Cosgrave).

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