摘要
利用差分的技巧给出了陈景润关于等幂和的两个递推公式的简单证明。由此递推公式得到S21(n)|S2m+1(n),S2(n)|S2m(n),同时给出了Bernoulli数B2k+1=0的又一证明。利用一对共轭式,给出陈景润关于等幂和的另一结论的简单证明。通过归纳,给出了等幂和的一个猜想。该猜想和Bernoulli数有着密切的联系。
Simple proofs of Chen's two recursion formulas on sums of powers of natural numbers are given by using the skill of differential.From those recursion formulas,the results S^(2)_(1)(n)|S_(2m+1)(n),S_(2)(n)|S_(2m)(n) and another proof for the 2k+1 th Bernoulli number B_(2k+1)=0 is given.Using a couple of conjugacy expressions,a simple proof of Chen's another theorem of sums of powers of natural numbers is offerred.By induction,a conjecture on sums of powers of natural numbers is reached and intimately connected with the Bernoulli numbers.
出处
《南京工业大学学报(自然科学版)》
CAS
2004年第6期45-47,66,共4页
Journal of Nanjing Tech University(Natural Science Edition)