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.

**[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 ." (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 . 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