On congruences related to trinomial coefficients and harmonic numbers
Yıl: 2021 Cilt: 45 Sayı: 4 Sayfa Aralığı: 1592 - 1604 Metin Dili: İngilizce DOI: 10.3906/mat-2101-128 İndeks Tarihi: 30-06-2022
On congruences related to trinomial coefficients and harmonic numbers
Öz: In this paper, we establish some congruences involving the trinomial coefficients and harmonic numbers. For
example, for any prime p > 3,
Σp−1
k=0
(−1)k
(
p − 1
k
)
2
Hk ≡ 0 (mod p).
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Andrews GE. Euler’s “exemplum memorabile inductionis fallacis” and q-trinomial coefficients. Journal of the American Mathematical Society 1990; 3: 653-669.
- [2] Apagodu M, Liu J-C. Congruence properties for the trinomial coefficients. Integers 2020; 20: A38 1-10.
- [3] Cao HQ, Pan H. Some congruences for trinomial coefficients. Houston Journal of Mathematics 2014; 40 (4): 1073- 1087.
- [4] Comtet L. Advanced Combinatorics. Dordrecht, The Netherlands: Reidel Publishing Company, 1974.
- [5] Elkhiri L, Koparal S, Ömür N. Some congruences and generalization of Meštrović’s congruence. Submitted for publication.
- [6] Elkhiri L, Mihoubi M. Super congruences involving trinomial coefficients. Arxiv: 1910.09262, submitted for publication.
- [7] Fahssi N. Some identities involving polynomial coefficients. The Fibonacci Quarterly 2016; 54: 125-136.
- [8] Freund JE. Restricted occupancy theory - A generalization of Pascal’s triangle. The American Mathematical Monthly 1956; 63 (1): 20-27.
- [9] Koparal S, Ömür N. On congruences related to central binomial coefficients, harmonic and Lucas numbers. Turkish Journal of Mathematics 2016; 40: 973-985.
- [10] Lehmer E. On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson. Annals of Mathematics 1938; 39: 350-360.
- [11] Mao GS, Sun ZW. Two congruences involving harmonic numbers with applications. International Journal of Number Theory 2016; 12 (2): 527-539.
- [12] Spieβ J. Some identities involving harmonic numbers. Mathematics of Computation 1990; 55(192): 839-863.
- [13] Sun ZW. Congruences involving generalized central trinomial coefficients. Science China Mathematics 2014; 57 (7): 1375-1400.
- [14] Sun ZW, Tauraso R. On some new congruences for binomial coefficients. International Journal of Number Theory 2011; 7: 645-662.
| APA | ömür n, koparal s, Elkhırı l (2021). On congruences related to trinomial coefficients and harmonic numbers. , 1592 - 1604. 10.3906/mat-2101-128 |
| Chicago | ömür neşe,koparal sibel,Elkhırı laıd On congruences related to trinomial coefficients and harmonic numbers. (2021): 1592 - 1604. 10.3906/mat-2101-128 |
| MLA | ömür neşe,koparal sibel,Elkhırı laıd On congruences related to trinomial coefficients and harmonic numbers. , 2021, ss.1592 - 1604. 10.3906/mat-2101-128 |
| AMA | ömür n,koparal s,Elkhırı l On congruences related to trinomial coefficients and harmonic numbers. . 2021; 1592 - 1604. 10.3906/mat-2101-128 |
| Vancouver | ömür n,koparal s,Elkhırı l On congruences related to trinomial coefficients and harmonic numbers. . 2021; 1592 - 1604. 10.3906/mat-2101-128 |
| IEEE | ömür n,koparal s,Elkhırı l "On congruences related to trinomial coefficients and harmonic numbers." , ss.1592 - 1604, 2021. 10.3906/mat-2101-128 |
| ISNAD | ömür, neşe vd. "On congruences related to trinomial coefficients and harmonic numbers". (2021), 1592-1604. https://doi.org/10.3906/mat-2101-128 |
| APA | ömür n, koparal s, Elkhırı l (2021). On congruences related to trinomial coefficients and harmonic numbers. Turkish Journal of Mathematics, 45(4), 1592 - 1604. 10.3906/mat-2101-128 |
| Chicago | ömür neşe,koparal sibel,Elkhırı laıd On congruences related to trinomial coefficients and harmonic numbers. Turkish Journal of Mathematics 45, no.4 (2021): 1592 - 1604. 10.3906/mat-2101-128 |
| MLA | ömür neşe,koparal sibel,Elkhırı laıd On congruences related to trinomial coefficients and harmonic numbers. Turkish Journal of Mathematics, vol.45, no.4, 2021, ss.1592 - 1604. 10.3906/mat-2101-128 |
| AMA | ömür n,koparal s,Elkhırı l On congruences related to trinomial coefficients and harmonic numbers. Turkish Journal of Mathematics. 2021; 45(4): 1592 - 1604. 10.3906/mat-2101-128 |
| Vancouver | ömür n,koparal s,Elkhırı l On congruences related to trinomial coefficients and harmonic numbers. Turkish Journal of Mathematics. 2021; 45(4): 1592 - 1604. 10.3906/mat-2101-128 |
| IEEE | ömür n,koparal s,Elkhırı l "On congruences related to trinomial coefficients and harmonic numbers." Turkish Journal of Mathematics, 45, ss.1592 - 1604, 2021. 10.3906/mat-2101-128 |
| ISNAD | ömür, neşe vd. "On congruences related to trinomial coefficients and harmonic numbers". Turkish Journal of Mathematics 45/4 (2021), 1592-1604. https://doi.org/10.3906/mat-2101-128 |
