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Mathematics of Computation

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



Three summation criteria for Fermat’s last theorem

Author: H. Schwindt
Journal: Math. Comp. 40 (1983), 715-716
MSC: Primary 10-04; Secondary 10B15
MathSciNet review: 689484
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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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Article copyright: © Copyright 1983 American Mathematical Society