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Gunderson's function in Fermat's last theorem


Authors: Daniel Shanks and H. C. Williams
Journal: Math. Comp. 36 (1981), 291-295
MSC: Primary 10-04; Secondary 10B15
DOI: https://doi.org/10.1090/S0025-5718-1981-0595065-7
MathSciNet review: 595065
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Abstract: We study Gunderson's function which gives a bound on the first case of Fermat's last theorem, assuming that the generalized Wieferich criterion is valid for the first n prime bases. We note two unexpected phenomena.


References [Enhancements On Off] (What's this?)

  • [1] J. Brillhart, J. Tonascia & P. Weinberger, "On the Fermat quotient," Computers in Number Theory, Academic Press, London, 1971, pp. 213-222. MR 0314736 (47:3288)
  • [2] D. H. Lehmer & Emma Lehmer, "Cyclotomy with $ \mu (n) = 0$." (To appear.)
  • [3] Norman G. Gunderson, Derivation of Criteria for the First Case of Fermat's Last Theorem and the Combination of These Criteria to Produce a New Lower Bound for the Exponent, Thesis, Cornell University, Sept. 1948.
  • [4] Daniel Shanks, Solved and Unsolved Problems in Number Theory, 2nd ed., Chelsea, New York, 1978, pp. 232, 233. Note added. In [5], D. H. Lehmer extends the data on (3) to $ 6 \cdot {10^9}$. There are no further solutions to that limit. Since the calculation was done ab initio, it also confirms the earlier calculation [1]. MR 516658 (80e:10003)
  • [5] D. H. Lehmer, "On Fermat's quotient, base two," Math. Comp., v. 36, 1981, pp. 289-290. MR 595064 (82e:10004)

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DOI: https://doi.org/10.1090/S0025-5718-1981-0595065-7
Article copyright: © Copyright 1981 American Mathematical Society

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