A congruence for primes
Author:
Zhi Wei Sun
Journal:
Proc. Amer. Math. Soc. 123 (1995), 13411346
MSC:
Primary 11A07; Secondary 11B68
DOI:
https://doi.org/10.1090/S0002993919951242105X
MathSciNet review:
1242105
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Abstract: With the help of the Pell sequence we obtain the following new congruence for odd primes: \[ \sum \limits _{k = 1}^{(p  1)/2} {\frac {1}{{k \cdot {2^k}}} \equiv \sum \limits _{k = 1}^{[3p/4]} {\;\frac {{{{(  1)}^{k  1}}}}{k}} \quad \pmod p.} \]

ZhiHong 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), 105118.
ZhiWei 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 numbertheoretical 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/aa604371388
 Andrew Granville and ZhiWei Sun, Values of Bernoulli polynomials, Pacific J. Math. 172 (1996), no. 1, 117–137. MR 1379289
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© Copyright 1995
American Mathematical Society