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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.
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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.

Information

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

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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