A congruence involving products of q-binomial coefficients
نویسندگان
چکیده
منابع مشابه
A CONGRUENCE INVOLVING PRODUCTS OF q-BINOMIAL COEFFICIENTS
In this paper we establish a q-analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime.
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For a positive composite integer n, we investigate the residues of ( mn k ) for positive integers m and k. First, we discuss divisibility of such coefficients. Then we study congruence identities relating products of binomial coefficients modulo n. Certainly the Chinese Remainder Theorem can be used in combination with prime power results to evaluate binomial coefficients modulo a composite. Ho...
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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: Journal of Number Theory
سال: 2006
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.02.004