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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A congruence for primes

Author: Zhi Wei Sun
Journal: Proc. Amer. Math. Soc. 123 (1995), 1341-1346
MSC: Primary 11A07; Secondary 11B68
MathSciNet review: 1242105
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Abstract: With the help of the Pell sequence we obtain the following new congruence for odd primes:

$\displaystyle \sum\limits_{k = 1}^{(p - 1)/2} {\frac{1}{{k \cdot {2^k}}} \equiv \sum\limits_{k = 1}^{[3p/4]} {\;\frac{{{{( - 1)}^{k - 1}}}}{k}} \quad \pmod p.} $

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PII: S 0002-9939(1995)1242105-X
Article copyright: © Copyright 1995 American Mathematical Society

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