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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
DOI: https://doi.org/10.1090/S0002-9939-1995-1242105-X
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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DOI: https://doi.org/10.1090/S0002-9939-1995-1242105-X
Article copyright: © Copyright 1995 American Mathematical Society

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