منابع مشابه
Two congruences involving 4-cores
γνωσι πoλλoυς αι µπνoιης The goal of this paper is to prove two new congruences involving 4–cores using elementary techniques; namely, if a 4 (n) denotes the number of 4–cores of n, then a 4 (9n+2) ≡ 0 (mod 2) and a 4 (9n + 8) ≡ 0 (mod 4).
متن کاملCongruences involving Bernoulli polynomials
Let {Bn(x)} be the Bernoulli polynomials. In the paper we establish some congruences for Bj(x) (mod p n), where p is an odd prime and x is a rational p-integer. Such congruences are concerned with the properties of p-regular functions, the congruences for h(−sp) (mod p) (s = 3, 5, 8, 12) and the sum P k≡r (mod m) p k , where h(d) is the class number of the quadratic field Q(d) of discriminant d...
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 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 کاملSome Congruences Involving Euler Numbers
In this paper, we obtain some explicit congruences for Euler numbers modulo an odd prime power in an elementary way.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1995
ISSN: 1077-8926
DOI: 10.37236/1268