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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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