New bound for the first case of Fermat's last theorem

Authors:
Jonathan W. Tanner and Samuel S. Wagstaff

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

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Abstract | References | Similar Articles | Additional Information

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 , unlike Gunderson's, and it increases more swiftly. Using the recent extension of the Wieferich criterion to 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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DOI:
https://doi.org/10.1090/S0025-5718-1989-0982371-4

Article copyright:
© Copyright 1989
American Mathematical Society