The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked
نویسندگان
چکیده
منابع مشابه
Congruences concerning Bernoulli numbers and Bernoulli polynomials
Let {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer’s congruences by determining Bk(p−1)+b(x)=(k(p − 1) + b) (modp), where p is an odd prime, x is a p-integral rational number and p − 1 b. As applications we obtain explicit formulae for ∑p−1 x=1 (1=x ) (modp ); ∑(p−1)=2 x=1 (1=x ) (modp ); (p − 1)! (modp ) and Ar(m;p) (modp), where k ∈ {1; 2; : : : ; p− 1} and Ar(m;p) i...
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ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2019
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2019.103009