Some congruences involving binomial coefficients
نویسندگان
چکیده
منابع مشابه
Some 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 −...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2015
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm139-1-8