Congruences involving Bernoulli and Euler numbers

作者：Sun Zhi Hong^*

来源：Journal of Number Theory, 2008, 128(2): 280-312.

DOI：10.1016/j.jnt.2007.03.003

• Congruence
• Bernoulli number
• Bernoulli polynomial
• Euler number

Let [x] be the integral part of x. Let p > 5 be a prime. In the paper we mainly determine Sigma([p/4])(x=1) 1/x(k) (mod p(2)), ((p-1)([p/4]))(mod p(3)), Sigma(p-1)(k=1)2(k/)k (mod p(3)) and Sigma(p-1)(k=1)2(k)/k(2) (mod p(2)) in terms of Euler and Bernoulli numbers. For example, we have
Sigma([p/4])(x=1)1/x(2) equivalent to (-1)(p-1/2)(8E(p-3) - 4E(2p-4)) + 14/3 pB(p-3) (mod p(2)),
where E(n) is the nth Euler number and B(n) is the nth Bernoulli number.

• 出版日期2008-2
• 单位南宁师范大学; 淮阴师范学院