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


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

    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. 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).
  • Zhi Hong Sun and Zhi Wei Sun, Fibonacci numbers and Fermat’s last theorem, Acta Arith. 60 (1992), no. 4, 371–388. MR 1159353, DOI https://doi.org/10.4064/aa-60-4-371-388
  • 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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Article copyright: © Copyright 1995 American Mathematical Society