Skip to main content
SpringerLink
Log in

On the First Case of the Fermat Theorem for Cyclotomic Fields

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  1. Z. I. Borevich andI. R. Shafarevich, Number Theory [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  2. D. Coppermith, “Fermat's last theorem (case 1) and the Weiferich criterion, ” Math. Comput., 54, 895-902 (1990).

    Google Scholar 

  3. M. Eichler, “Eine Bemerkung zur Fermat'schen Vermutung, ” Acta Arithm., 11, 129-131 (1965).

    Google Scholar 

  4. A. Granville andM. B. Monogan, “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 (1988).

    Google Scholar 

  5. K. Iwasawa, “On explicit formulas for the norm residue symbol, ” J. Math. Soc. Jpn., 20, 151-164 (1968).

    Google Scholar 

  6. W. Keller andG. Löh, “The criteria of Kummer and Mirimano. extended to include 22 consecutive irregular pairs, ” Tokyo J. Math., 6, 397-402 (1983).

    Google Scholar 

  7. V. A. Kolyvagin, “The Fermat equations over cyclotomic fields, ” Tr. V. A. Steklov Mat. Inst., 208, 163-185 (1995).

    Google Scholar 

  8. M. Krasner, “Sur le premier cas du théorème de Fermat, ” C. R. Acad. Sci. Paris, 199, 256-258 (1934).

    Google Scholar 

  9. E. E. Kummer, “Einige Sätze über die aus den Wurzeln der Gleichung αλ = 1 gebildeten complexen Zahlen, für den Fall class die Klassensahl durch λ theilbar ist, nebst Anwendungen derselben auf einen weiteren Beweis des letztes Fermat'schen Lehrsatzes, ” In: Math. Abh. Akad. Wiss. Berlin (1857), pp. 41-74.

  10. D. Mirimanoff, “L'équation indéterminée xl + yl + zl = 0 et le criterium de Kummer, ” J. Reine Angew. Math., 128, 45-68 (1905).

    Google Scholar 

  11. J. H. Silverman, “Wieferich's criterion and the abc-conjecture, ” J. Number Theory, 30, 226-237 (1988).

    Google Scholar 

  12. H. S. Vandiver, “Laws of reciprocity and the first case of Fermat's last theorem, ” Proc. Natl. Acad. Sci. U.S.A., 11, 292-298 (1925).

    Google Scholar 

  13. S. S.Wagsta., “The irregular prime to 125000, ” Math. Comput., 32, 583-591 (1978).

    Google Scholar 

  14. A. Wieferich, “Zum letzten Fermat'schen Theorem, ” J. Reine Angew. Math., 136, 293-302 (1909).

    Google Scholar 

  15. A. Wiles, “Modular curves and Fermat's last theorem, ” Ann. Math., 142, 443-351 (1995).

    Google Scholar 

Download references

Authors
  1. V. A. Kolyvagin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kolyvagin, V.A. On the First Case of the Fermat Theorem for Cyclotomic Fields. Journal of Mathematical Sciences 106, 3302–3311 (2001). https://doi.org/10.1023/A:1017955309615

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1017955309615

Keywords

Search

Navigation