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Mathematics of Computation

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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: 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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DOI: https://doi.org/10.1090/S0025-5718-1989-0982371-4
Article copyright: © Copyright 1989 American Mathematical Society