Research Article

Some Congruences for Sums Involving Harmonic Numbers

Volume: 39 Number: 4 December 24, 2018
TR EN

Some Congruences for Sums Involving Harmonic Numbers

Abstract

In this paper, we establish some congruences involving sums with harmonic numbers and the terms of second-order linear sequences.

Keywords

References

  1. [1] Granville A., The square of the Fermat quotient, Integers: Electronic Journal of Combinatorial Number Theory, 4 (2004) #A22.
  2. [2] Kılıç E., Ömür N. and Türker Ulutaş Y., Alternating sums of the powers of Fibonacci and Lucas numbers, Miskolc Math. Notes, 12-1 (2011) 87-103.
  3. [3] Kılıç E., Ömür N. and Türker Ulutaş, Y., Some finite sums involving generalized Fibonacci and Lucas numbers, Discrete Dynamics in Nature and Society, (2011) 1-11, doi:10.1155/2011/284261.
  4. [4] Koparal S. and Ömür N., On congruences related to central binomial coefficients, harmonic and Lucas numbers, Turkish Journal of Mathematics, 40 (2016) 973-985.
  5. [5] Melham R.S., Certain classes of finite sums that involve generalized Fibonacci and Lucas numbers, The Fibonacci Quarterly, 42-1 (2004) 47–54.
  6. [6] Ömür N. and Koparal S., Some congruences related to harmonic numbers and the terms of the second order sequences, Mathematica Moravica, 20 (2016) 23-37.
  7. [7] Sun Z.W., Arithmetic theory of harmonic numbers, Proc. Amer. Math. Soc., 140-2 (2012) 415-428.
  8. [8] Sun Z.W. and Zhao L.L., Arithmetic theory of harmonic numbers (II), Colloq. Math., 130-1 (2013) 67-78.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Neşe Ömür
Türkiye

Publication Date

December 24, 2018

Submission Date

September 21, 2018

Acceptance Date

November 1, 2018

Published in Issue

Year 2018 Volume: 39 Number: 4

APA
Koparal, S., & Ömür, N. (2018). Some Congruences for Sums Involving Harmonic Numbers. Cumhuriyet Science Journal, 39(4), 912-919. https://doi.org/10.17776/csj.462331

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December