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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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Three summation criteria for Fermat’s last theorem
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by H. Schwindt PDF
Math. Comp. 40 (1983), 715-716 Request permission

Abstract:

This paper extends the search for solutions of the congruences \[ \sum \limits _1^{[p/6]} {\frac {1}{i} \equiv 0,} \quad \sum \limits _1^{[p/6]} {\frac {1}{{{i^2}}} \equiv 0} \quad {\text {and}}\quad \sum \limits _{[p/6] + 1}^{[p/5]} {\frac {1}{i} \equiv 0\;\pmod p} \] to the limit $p < 600000$. The only solutions found were $p = 61$ in the first case, in the second $p = 205129$, and in the third case $p = 109$ and $p = 491$.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 715-716
  • MSC: Primary 10-04; Secondary 10B15
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0689484-X
  • MathSciNet review: 689484