Some Congruences for Sums Involving Harmonic Numbers

Araştırma Makalesi

Yıl 2018, Cilt: 39 Sayı: 4, 912 - 919, 24.12.2018

Sibel Koparal , Neşe Ömür

https://doi.org/10.17776/csj.462331

Bu makalede harmonik sayıları ve ikinci mertebeden lineer dizilerin
terimlerini içeren toplamlar hakkında bazı denklikler gösterilmiştir.

[1] Granville A., The square of the Fermat quotient, Integers: Electronic Journal of Combinatorial Number Theory, 4 (2004) #A22.
[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] 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] 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] Melham R.S., Certain classes of finite sums that involve generalized Fibonacci and Lucas numbers, The Fibonacci Quarterly, 42-1 (2004) 47–54.
[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] Sun Z.W., Arithmetic theory of harmonic numbers, Proc. Amer. Math. Soc., 140-2 (2012) 415-428.
[8] Sun Z.W. and Zhao L.L., Arithmetic theory of harmonic numbers (II), Colloq. Math., 130-1 (2013) 67-78.
[9] Wolstenholme J., On certain properties of prime numbers, Quart. J. Math., 5 (1862) 35-39.

Yıl 2018, Cilt: 39 Sayı: 4, 912 - 919, 24.12.2018

Sibel Koparal , Neşe Ömür

https://doi.org/10.17776/csj.462331

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

[1] Granville A., The square of the Fermat quotient, Integers: Electronic Journal of Combinatorial Number Theory, 4 (2004) #A22.
[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] 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] 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] Melham R.S., Certain classes of finite sums that involve generalized Fibonacci and Lucas numbers, The Fibonacci Quarterly, 42-1 (2004) 47–54.
[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] Sun Z.W., Arithmetic theory of harmonic numbers, Proc. Amer. Math. Soc., 140-2 (2012) 415-428.
[8] Sun Z.W. and Zhao L.L., Arithmetic theory of harmonic numbers (II), Colloq. Math., 130-1 (2013) 67-78.
[9] Wolstenholme J., On certain properties of prime numbers, Quart. J. Math., 5 (1862) 35-39.

Toplam 9 adet kaynakça vardır.

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