On congruences related to central binomial coefficients, harmonic and Lucas numbers

ÖMÜR, Neşe; koparal, sibel

On congruences related to central binomial coefficients, harmonic and Lucas numbers

Sibel KOPARAL, (Kocaeli Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Kocaeli, İzmit, Türkiye)

Neşe ÖMÜR (Kocaeli Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Kocaeli, İzmit, Türkiye)

Turkish Journal of Mathematics

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Yıl: 2016 Cilt: 40 Sayı: 5 Sayfa Aralığı: 973 - 985 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

On congruences related to central binomial coefficients, harmonic and Lucas numbers

Öz:

In this paper, using some combinatorial identities, we present new congruences involving central binomial coefficients and harmonic, Catalan, and Fibonacci numbers. For example, for an odd prime p, we have (p∑−1)/2 k=1 (−1)k ( 2k k ) Hk−1 ≡ 2 p p ( 2Fp+1 − 5 (p−1)/2 − 1 ) (mod p), (p∑−1)/2 k=0 HkCk (−4)k ≡ 2 Qp+1 p − 2 p+1 p ( 1 + 2(p+1)/2 ) (mod p), and for ( 5 p ) = 1, (p∑−1)/2 k=1 ( 2k k ) Hk−1Fk (−4)k ≡ 1 p (F2p+1 − Fp+2) − 2 p p Fp−1(mod p), where {Fn} is the Fibonacci sequence and {Qn} is the Pell Lucas sequence.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	koparal s, ÖMÜR N (2016). On congruences related to central binomial coefficients, harmonic and Lucas numbers. , 973 - 985.
Chicago	koparal sibel,ÖMÜR Neşe On congruences related to central binomial coefficients, harmonic and Lucas numbers. (2016): 973 - 985.
MLA	koparal sibel,ÖMÜR Neşe On congruences related to central binomial coefficients, harmonic and Lucas numbers. , 2016, ss.973 - 985.
AMA	koparal s,ÖMÜR N On congruences related to central binomial coefficients, harmonic and Lucas numbers. . 2016; 973 - 985.
Vancouver	koparal s,ÖMÜR N On congruences related to central binomial coefficients, harmonic and Lucas numbers. . 2016; 973 - 985.
IEEE	koparal s,ÖMÜR N "On congruences related to central binomial coefficients, harmonic and Lucas numbers." , ss.973 - 985, 2016.
ISNAD	koparal, sibel - ÖMÜR, Neşe. "On congruences related to central binomial coefficients, harmonic and Lucas numbers". (2016), 973-985.

APA	koparal s, ÖMÜR N (2016). On congruences related to central binomial coefficients, harmonic and Lucas numbers. Turkish Journal of Mathematics, 40(5), 973 - 985.
Chicago	koparal sibel,ÖMÜR Neşe On congruences related to central binomial coefficients, harmonic and Lucas numbers. Turkish Journal of Mathematics 40, no.5 (2016): 973 - 985.
MLA	koparal sibel,ÖMÜR Neşe On congruences related to central binomial coefficients, harmonic and Lucas numbers. Turkish Journal of Mathematics, vol.40, no.5, 2016, ss.973 - 985.
AMA	koparal s,ÖMÜR N On congruences related to central binomial coefficients, harmonic and Lucas numbers. Turkish Journal of Mathematics. 2016; 40(5): 973 - 985.
Vancouver	koparal s,ÖMÜR N On congruences related to central binomial coefficients, harmonic and Lucas numbers. Turkish Journal of Mathematics. 2016; 40(5): 973 - 985.
IEEE	koparal s,ÖMÜR N "On congruences related to central binomial coefficients, harmonic and Lucas numbers." Turkish Journal of Mathematics, 40, ss.973 - 985, 2016.
ISNAD	koparal, sibel - ÖMÜR, Neşe. "On congruences related to central binomial coefficients, harmonic and Lucas numbers". Turkish Journal of Mathematics 40/5 (2016), 973-985.