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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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New bound for the first case of Fermat’s last theorem
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by Jonathan W. Tanner and Samuel S. Wagstaff PDF
Math. Comp. 53 (1989), 743-750 Request permission

Abstract:

We present an improvement to Gunderson’s function, which gives a lower bound for the exponent in a possible counterexample to the first case of Fermat’s "Last Theorem," assuming that the generalized Wieferich criterion is valid for the first n prime bases. The new function increases beyond $n = 29$, unlike Gunderson’s, and it increases more swiftly. Using the recent extension of the Wieferich criterion to $n = 24$ by Granville and Monagan, the first case of Fermat’s "Last Theorem" is proved for all prime exponents below 156, 442, 236, 847, 241, 729.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 743-750
  • MSC: Primary 11D41; Secondary 11Y50
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0982371-4
  • MathSciNet review: 982371