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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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


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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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 54 (1990), 895-902
  • MSC: Primary 11D41
  • DOI:
  • MathSciNet review: 1010598