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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A congruence for primes
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by Zhi Wei Sun PDF
Proc. Amer. Math. Soc. 123 (1995), 1341-1346 Request permission

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
    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 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, DOI 10.2140/pjm.1996.172.117
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • 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