| 摘要: |
| 获得了等幂和与Bernoulli数的同余关系,利用所得到的结果对Bowen猜想进行了讨论,得:若方程Sm(n)=(n+1)m有m >1的解,则m≥28为偶数,6nBm≡ 6(mn+1)(mod n2),n=2p1p2…pS,pi-1|m,(n/pi)≡ m((pi-1)!+pi+1)-pi-1(mod pi2). |
| 关键词: 等幂和 Bernoulli数 Bowen猜想 |
| DOI： |
| 投稿时间：1999-06-22 |
| 基金项目:第四届全国初等数学研究学术交流会学术报告和广西民族学院重点科研项目资助课题。 |
|
| On the Bernoulli Numbers and Bowen's Conjecture |
|
Wang Yunkui
|
| (Dept. of Math. & Comp. Sci., Guangxi Univ. for Nationalities, Xixiangtang, Nanning, Guangxi, 530006, China) |
| Abstract: |
| We gain congruences relation of sum of equal powers and Bernoulli's numbers,and Bowen's conjecture was discussed by using our theorems on the structure of Bernoulli's numbers,Acquired that if Sm(n)=(n +1)m and m>1,then m ≥ 28 is an even number, 6nBm≡6(mn+1)(mod n2),n=2p1p2…ps,pi-1 dividing of m,(n/pi)≡m((pi-1)!+pi+1)-pi-1(mod pi2). |
| Key words: sum of equal powers Bernoulli's numbers Bowen's conjecture |
