TY  - JOUR
TI  - On congruences related to central binomial coefficients, harmonic and Lucas numbers
AB  - 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.
AU  - ÖMÜR, Neşe
AU  - koparal, sibel
PY  - 2016
JO  - Turkish Journal of Mathematics
VL  - 40
IS  - 5
SN  - 1300-0098
SP  - 973
EP  - 985
DB  - TRDizin
UR  - http://search/yayin/detay/245307
ER  -