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Mathematics of Computation

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



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

Author: Don Coppersmith
Journal: Math. Comp. 54 (1990), 895-902
MSC: Primary 11D41
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 $7.568 \times {10^{17}}$.

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Article copyright: © Copyright 1990 American Mathematical Society