ON SOME NEW CONGRUENCES FOR BINOMIAL COEFFICIENTS
نویسندگان
چکیده
منابع مشابه
On Some New Congruences for Binomial Coefficients
In this paper we establish some new congruences involving central binomial coefficients as well as Catalan numbers. Let p be a prime and let a be any positive integer. We determine ∑pa−1 k=0 ( 2k k+d ) mod p2 for d = 0, . . . , pa and ∑pa−1 k=0 ( 2k k+δ ) mod p3 for δ = 0, 1. We also show that
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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 ∑
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2011
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042111004393