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, and P. Weinberger,*On the Fermat quotient*, Computers in number theory (Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969) Academic Press, London, 1971, pp. 213–222. MR**0314736****[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 Publishing Co., New York, 1978. MR**516658****[5]**D. H. Lehmer,*On Fermat’s quotient, base two*, Math. Comp.**36**(1981), no. 153, 289–290. MR**595064**, https://doi.org/10.1090/S0025-5718-1981-0595064-5

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0595065-7

Article copyright:
© Copyright 1981
American Mathematical Society