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

Coppersmith, Don

doi:10.1090/S0025-5718-1990-1010598-2

Fermat’s last theorem (case $1$) and the Wieferich criterion
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Math. Comp. 54 (1990), 895-902 Request permission

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

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Derivation of criteria for the first case of Fermat’s last theorem and the combination of these criteria to produce a new lower bound for the exponent

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