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On the congruences $ (p-1)!\equiv -1$ and $ 2\sp{p-1}\equiv 1\,({\rm mod}\,p\sp{2})$


Author: Erna H. Pearson
Journal: Math. Comp. 17 (1963), 194-195
MSC: Primary 10.06
DOI: https://doi.org/10.1090/S0025-5718-1963-0159780-0
MathSciNet review: 0159780
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References [Enhancements On Off] (What's this?)

  • [1] N. G. W. H. Beeger, ``On the congruence $ (p - 1)! \equiv - 1(\bmod {p^2})$,'' Mess. of Math. v. 49, 1920, p. 177-178.
  • [2] Emma Lehmer, ``A note on Wilson's quotient,'' Am. Math. Month., v. 44, 1937, p. 237 and 462.
  • [3] K. Goldberg, ``Table of Wilson quotients and the third Wilson prime,'' Proc. London Math. Soc., v. 28, 1953, p. 252-256. MR 0055358 (14:1062d)
  • [4] C. E. Froberg, ``Some computations of Wilson and Fermat remainders,'' MTAC, v. 12, 1958, p. 281.
  • [5] S. Kravitz, ``The congruence $ {2^{p - 1}} \equiv (\bmod {p^2})$ for $ p\, < \,100,000$,'' Math. Comp., v. 14, 1960, p. 378. MR 0121334 (22:12073)
  • [6] G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers, Third Edition. London, Oxford, 1954, p. 106. MR 0067125 (16:673c)

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DOI: https://doi.org/10.1090/S0025-5718-1963-0159780-0
Article copyright: © Copyright 1963 American Mathematical Society

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