| 多重调和级数的几个同余式 |
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| 引用本文： | 沈忠燕.多重调和级数的几个同余式[J].浙江教育学院学报,2011(5):91-95. |
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| 作者姓名： | 沈忠燕 |
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| 作者单位： | 浙江外国语学院理工学院,浙江杭州,310012 |
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| 摘 要： | 通过研究∑l1＋l2＋…＋ln=p σln/l1…ln-1lkn,σ∈{-1,1}的同余式,当k=2,3时,对任意的正整数n和素数p〉n＋k-1,得到了∑l1＋l2＋…＋ln=p 1/l1l2…lkn关于模p的同余式.对任意的素数p≥7,证明了∑l1＋l2＋l3＋l4=p （-1）l1/l1l2l3l4关于模的同余式.
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| 关 键 词： | Bernoulli数 调和级数 同余式 |
Some Congruences Involving Multiple Harmonic Sums |
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| SHEN Zhongyan.Some Congruences Involving Multiple Harmonic Sums[J].Journal of ZHEJIANG Education Institute,2011(5):91-95. |
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| Authors: | SHEN Zhongyan |
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| Institution: | SHEN Zhongyan (Shool of Science and Technology,Zhejiang International Studies University,Hangzhou 310012,China) |
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| Abstract: | Study the conguences for ∑l1＋l2＋…＋ln=p σln/l1…ln-1lkn,σ∈{1,-1},and when k=2,3,for all positive number and prime pn＋k-1,congruences of ∑l1＋l2＋…＋ln=p 1/l1l2…lkn modulo prime p are obtained.For any prime p≥7,congruence of ∑l1＋l2＋l3＋l4=p（-1）l1/l1l2l3l4 modulo prime p is proved. |
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| Keywords: | Bernoulli numbers harmonic sums congruence |
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