Lower bounds for the solutions in the second case of Fermat’s last theorem
HTML articles powered by AMS MathViewer
- by Mao Hua Le
- Proc. Amer. Math. Soc. 111 (1991), 921-923
- DOI: https://doi.org/10.1090/S0002-9939-1991-1049137-1
- PDF | Request permission
Abstract:
Let $p$ be an odd prime. In this paper, we prove that if $p \equiv 3$ and $x,y,z$ are integers satisfying ${x^p} + {y^p} = {z^p},p|xyz,0 < x < y < z$, then $y > {2^{ - 1/p}}{p^{6p - 2}}$ and $z - x > \tfrac {1}{2}{p^{6p - 3}}$.References
- K. Inkeri, Abschätzungen für eventuelle Lösungen der Gleichung im Fermatschen Problem, Ann. Univ. Turku. Ser. A. 16 (1953), no. 1, 9 (German). MR 0058629 —, Remarks on Fermat’s equation: The very knowledge of coding, Univ. Turku, Turku, 1987, pp. 82-87.
- Rudolf Lidl and Harald Niederreiter, Finite fields, Encyclopedia of Mathematics and its Applications, vol. 20, Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. With a foreword by P. M. Cohn. MR 746963
- Paulo Ribenboim, 13 lectures on Fermat’s last theorem, Springer-Verlag, New York-Heidelberg, 1979. MR 551363
- H. S. Vandiver, A property of cyclotomic integers and its relation to Fermat’s last theorem, Ann. of Math. (2) 21 (1919), no. 2, 73–80. MR 1503604, DOI 10.2307/2007222
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 921-923
- MSC: Primary 11D41
- DOI: https://doi.org/10.1090/S0002-9939-1991-1049137-1
- MathSciNet review: 1049137