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Fermat's last theorem (case $ 1$) and the Wieferich criterion


Author: Don Coppersmith
Journal: Math. Comp. 54 (1990), 895-902
MSC: Primary 11D41
DOI: https://doi.org/10.1090/S0025-5718-1990-1010598-2
MathSciNet review: 1010598
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Abstract: This note continues work by the Lehmers [3], Gunderson [2], Granville and Monagan [1], and Tanner and Wagstaff [6], producing lower bounds for the prime exponent p in any counterexample to the first case of Fermat's Last Theorem. We improve the estimate of the number of residues $ r\bmod {p^2}$ such that $ {r^p} \equiv r\bmod {p^2}$, and thereby improve the lower bound on p to $ 7.568 \times {10^{17}}$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1990-1010598-2
Article copyright: © Copyright 1990 American Mathematical Society

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