On a conjecture of the Euler numbers

[摘要] The main purpose of this paper is to prove a conjecture of the Euler numbers and its generalization by using the analytic methods. That is, for any prime p = 1 (mod 4) and integer alpha >= 1 we proved E phi p (p(alpha))/2 not equivalent to 0 (mod p(alpha)), where E-2n are the Euler numbers and phi(n) the Euler function. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-01

[关键词] the Euler numbers;conjecture;analytic method;congruence