Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the generalized Wieferich criteria

Jiro Suzuki

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 70, Number 7 (1994), 230-234.

Dates
First available: 19 November 2007

Permanent link to this document
http://projecteuclid.org/euclid.pja/1195510946

Mathematical Reviews number (MathSciNet)
MR1303569

Zentralblatt MATH identifier
0834.11013

Digital Object Identifier
doi:10.3792/pjaa.70.230

Subjects
Primary: 11D41: Higher degree equations; Fermat's equation
Secondary: 11Y50: Computer solution of Diophantine equations

Citation

Suzuki, Jiro. On the generalized Wieferich criteria. Proceedings of the Japan Academy, Series A, Mathematical Sciences 70 (1994), no. 7, 230--234. doi:10.3792/pjaa.70.230. http://projecteuclid.org/euclid.pja/1195510946.


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References

  • [1] Coppersmith, D.: Fermat's last theorem (case 1) and the Wieferich criterion. Math. Comp., 54, 895-902 (1990).
  • [2] Granville, A., and Monagan, B.: The first case of Fermat's last, theorem is true for all prime exponents up to 714,591,416,091,389. Trans. Amer. Math. Soc., 306, 329-359 (1987).
  • [3] Gunderson, N. G.: 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 (1948).
  • [4] Lehmer, D. H.: On Fermat's quotient, base two. Math. Comp., 36, 289-290 (1981).
  • [5] Pollaczek, F.: Uber den grOssen Fermat'schen Satz. Wien. Berichte. Abt. Ha, 126, 45-59 (1917).
  • [6] Suzuki, J.: On the generalized Wieferich criteria for the first case of Fermat's last theorem (in preparation).