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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
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.} $


References [Enhancements On Off] (What's this?)

  • [1] Zhi-Hong Sun, Combinatorial sum $ \sum\nolimits_{k = 0,k \equiv r \pmod m}^n {\left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array} } \right)} $ and its applications in number theory (II), J. Nanjing Univ. Math. Biquarterly 10 (1993), 105-118.
  • [2] Zhi-Wei Sun, On the combinatorial sum $ \sum\nolimits_{k = 0,k \equiv r \pmod {12}}^n {\left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array} } \right)} $ and its number-theoretical applications (to appear).
  • [3] Zhi Hong Sun and Zhi Wei Sun, Fibonacci numbers and Fermat’s last theorem, Acta Arith. 60 (1992), no. 4, 371–388. MR 1159353
  • [4] Andrew Granville and Zhi-Wei Sun, Values of Bernoulli polynomials, Pacific J. Math. 172 (1996), no. 1, 117–137. MR 1379289

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Additional Information

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