Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T07:51:29.805Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the Fermat equation

Published online by Cambridge University Press:  26 February 2010

C. L. Stewart
C. L. Stewart
Affiliation:
Mathematisch Centrum, Amsterdam, The Netherlands.
Get access

Extract

Let x, y, z and n denote positive integers with x < y < z and (x, y, z) = 1. The purpose of this note is to prove two theorems, the first of which is

THEOREM 1. for some positive number Co, and if

then n is less than C, a number which is effectively computable in terms of Co.

Type
Research Article
Information
Mathematika , Volume 24 , Issue 1 , June 1977 , pp. 130 - 132
Copyright
Copyright © University College London 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Artin, E.. “The orders of the linear groups ”, Comm. Pure Appl. Math., 8 (1955), 355–366.CrossRefGoogle Scholar
2.Baker, A.. “Bounds for the solutions of the hyperelliptic equation ”, Proc. Camb. Phil. Soc., 65 (1969), 439–144.CrossRefGoogle Scholar
3.Baker, A.. “The theory of linear forms in logarithms ”, Transcendence Theory: Advances and Applications (Academic Press, London and New York, 1977).Google Scholar
4.Birkhoff, G. D. and Vandiver, H. S.. “On the integral divisors of an–bn ”, Ann. of Math., (2), 5 (1904), 173–180.CrossRefGoogle Scholar
5.Everett, C. J.. “Fermat's conjecture, Roth's theorem, Pythagorean triangles and Pell's equation ”, Duke Math. J., 40 (1973), 801–804.CrossRefGoogle Scholar
6.Inkeri, K.. “A note on Fermat's conjecture ”, Acta Arith, 29 (1976), 251–256.CrossRefGoogle Scholar
7.Wagstaff, S. S.. “Fermat's last theorem is true for any exponent less than 100,000 ”, Notices Amer. Math. Soc., 23 (1976), A–53.Google Scholar