关于Bernoulli数与Euler数的一组同余式

On A Group of Congruence of Bernoulli Number and Euler Number

进一步研究了Bernoulli数与Euler数的分布及其性质,使得在组合数学中Ber-noulli数与Euler数组合恒等式的研究取得显著成效并得到广泛应用.运用了初等数论中同余的理论和解析数论的方法.得出了Bernoulli数与Euler数的同余恒等式,简单的表达了Bernoulli数与Euler数的计算公式.利用同余理论,研究了Bernoulli数与Euler数的p≡3(mod4)的恒等式,从而还可以得到Bernoulli数与Euler数的关于p≡1,3(mod8)的恒等式.

To further study the distribution and properties of Bernoulli number and Euler number,and help combined identity of Bernoulli number and Euler number in combinatorics to make great achievements and wide application.The congruence theory in primary number theory and analytic number theory are applied.The congruence identity of Bernoulli number and Euler number is obtained,and computing formula for Bernoulli number and Euler number is simply expressed.With the application of congruence theory,the identity of p≡3（mod 4） of Bernoulli number and Euler number is studied,and the identity of p≡1,3（mod 8） of Bernoulli number and Euler number is obtained.