An Introduction to Gauss Factorials

@article{Cosgrave2011AnIT,
  title={An Introduction to Gauss Factorials},
  author={J. B. Cosgrave and K. Dilcher},
  journal={The American Mathematical Monthly},
  year={2011},
  volume={118},
  pages={812 - 829}
}
Abstract Starting with Wilson's theorem and its generalization by Gauss, we define a Gauss factorial Nn! to be the product of all positive integers up to N that are relatively prime to n. We present results on the 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. Finally, extensions of the Gauss binomial coefficient theorem are presented in terms of Gauss factorials. 
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