Some congruences involving central q-binomial coefficients
نویسندگان
چکیده
Motivated by recent works of Sun and Tauraso, we prove some variations on the Green-Krammer identity involving central q-binomial coefficients, such as n−1 ∑ k=0 (−1)kq−(k+1 2 ) [ 2k k ] q ≡ (n 5 ) q−bn 4/5c (mod Φn(q)), where ( n p ) is the Legendre symbol and Φn(q) is the nth cyclotomic polynomial. As consequences, we deduce that 3am−1 ∑
منابع مشابه
Some Congruences for Central Binomial Sums Involving Fibonacci and Lucas Numbers
We present several polynomial congruences about sums with central binomial coefficients and harmonic numbers. In the final section we collect some new congruences involving Fibonacci and Lucas numbers.
متن کاملCongruences Involving Binomial Coefficients and Lucas Sequences
In this paper we obtain some congruences involving central binomial coefficients and Lucas sequences. For example, we show that if p > 5 is a prime then p−1
متن کاملSome Congruences Involving Binomial Coefficients
Binomial coefficients and central trinomial coefficients play important roles in combinatorics. Let p > 3 be a prime. We show that Tp−1 ≡ (p 3 ) 3p−1 (mod p), where the central trinomial coefficient Tn is the constant term in the expansion of (1 + x + x−1)n. We also prove three congruences modulo p conjectured by Sun, one of which is p−1 ∑ k=0 ( p− 1 k )( 2k k ) ((−1) − (−3)−k) ≡ (p 3 ) (3p−1 −...
متن کاملCongruences Involving Catalan Numbers
In this paper we establish some new congruences involving Catalan numbers as well as central binomial coefficients. Let p > 3 be a prime. We show that
متن کامل, arXiv : 0709 . 1665 CONGRUENCES INVOLVING CATALAN NUMBERS
In this paper we establish some new congruences involving Catalan numbers as well as central binomial coefficients. Let p > 3 be a prime and let a be any positive integer. We show that
متن کامل