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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A role for generalized Fermat numbers
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by John B. Cosgrave and Karl Dilcher PDF
Math. Comp. 86 (2017), 899-933 Request permission


We define a Gauss factorial $N_n!$ to be the product of all positive integers up to $N$ that are relatively prime to $n\in \mathbb N$. In this paper we study particular aspects of the Gauss factorials $\lfloor \frac {n-1}{M}\rfloor _n!$ for $M=3$ and 6, where the case of $n$ having exactly one prime factor of the form $p\equiv 1\pmod {6}$ is of particular interest. A fundamental role is played by those primes $p\equiv 1\pmod {3}$ with the property that the order of $\frac {p-1}{3}!$ modulo $p$ is a power of 2 or 3 times a power of 2; we call them Jacobi primes. Our main results are characterizations of those $n\equiv \pm 1\pmod {M}$ of the above form that satisfy $\lfloor \frac {n-1}{M}\rfloor _n!\equiv 1\pmod {n}$, $M=3$ or 6, in terms of Jacobi primes and certain prime factors of generalized Fermat numbers. We also describe the substantial and varied computations used for this paper.
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Additional Information
  • John B. Cosgrave
  • Affiliation: 79 Rowanbyrn, Blackrock, County Dublin, A94 FF86, Ireland
  • Email:
  • Karl Dilcher
  • Affiliation: Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada
  • Email:
  • Received by editor(s): July 13, 2015
  • Received by editor(s) in revised form: August 6, 2015, September 9, 2015, and September 14, 2015
  • Published electronically: April 26, 2016
  • Additional Notes: This research was supported in part by the NSERC (Canada)
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 899-933
  • MSC (2010): Primary 11A07; Secondary 11B65
  • DOI:
  • MathSciNet review: 3584554