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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

A special extension of Wieferich's criterion


Author: Petr Cikánek
Journal: Math. Comp. 62 (1994), 923-930
MSC: Primary 11D41; Secondary 11Y40
MathSciNet review: 1216257
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Abstract | References | Similar Articles | Additional Information

Abstract: The following theorem is proved in this paper: "If the first case of Fermat's Last Theorem does not hold for sufficiently large prime l, then

$\displaystyle \sum\limits_x {{x^{l - 2}}} \left[ {\frac{{kl}}{N} < x < \frac{{(k + 1)l}}{N}} \right] \equiv 0\quad \pmod l$

for all pairs of positive integers $ N, k,N \leq 94, 0 \leq k \leq N - 1$." The proof of this theorem is based on a recent paper of Skula and uses computer techniques.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1216257-9
PII: S 0025-5718(1994)1216257-9
Keywords: The first case of Fermat's Last Theorem, Fermat quotient, Bernoulli numbers, Bernoulli polynomials
Article copyright: © Copyright 1994 American Mathematical Society