| Lehmer型同余式在多重调和级数上的推广 |
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| 引用本文： | 陈笑缘. Lehmer型同余式在多重调和级数上的推广[J]. 杭州师范学院学报(自然科学版), 2008, 7(5): 327-329 |
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| 作者姓名： | 陈笑缘 |
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| 作者单位： | 浙江商业职业技术学院基础部,浙江杭州310053 |
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| 摘 要： | 证明了若a为正整数且满足2na≤p-4,则∑ 1≤ll〈…ln≤p-1/2 1/ll^2a…ln^2a≡（-1）n＋1 1/n（1-1/2^2na＋1）2^2na 2na/2na＋1 Bp-a-1p（mod p^2）其中a=2a1＋…＋2an.推广了Lehmer关于幂次和的一类同余式，同时给出更多关于调和级数的同余式．
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| 关 键 词： | 多重调和级数 同余式 Bernoulli数 |
The Generalization of the Type of the Lehmer's Congruence on Multiple Harmonic Sums |
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| Chen Xiao-yuan. The Generalization of the Type of the Lehmer's Congruence on Multiple Harmonic Sums[J]. Journal of Hangzhou Teachers College(Natural Science), 2008, 7(5): 327-329 |
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| Authors: | Chen Xiao-yuan |
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| Affiliation: | CHEN Xiao-yuan (Department of Basic Courses, Zhejiang Vocational College of Commerce, Hangzhou 310053 ,China) |
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| Abstract: | The paper proves that if a is positive integer satisfing 2na≤p-4,then ∑ 1≤ll〈…ln≤p-1/2 1/ll^2a…ln^2a≡（-1）n＋1 1/n（1-1/2^2na＋1）2^2na 2na/2na＋1 Bp-a-1p（mod p^2）,where a=2a1＋…＋2an This generalizes a class of congruences involving the harmonic sums obtained by Lehmer. The paper also shows more congruences on harmonic sums. |
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| Keywords: | multiple harmonic sums congruences Bernoulli numbers |
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