| Fermat小定理的推广及其应用 |
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| 引用本文： | 张敏,李金蒋,居腾霞. Fermat小定理的推广及其应用[J]. 徐州师范大学学报(自然科学版), 2012, 30(4): 1-5 |
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| 作者姓名： | 张敏 李金蒋 居腾霞 |
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| 作者单位： | 南通大学理学院数学系,江苏南通,226007 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 利用映射的不动点以及不动点阶的思想将整数环Z上的Fermat小定理推广到一般集合S上,并运用该推广讨论了Dirichlet定理的一种特殊情形：只要给定正整数m≥3,那么算术数列1＋lm（l=0,1,2,…）中一定存在无穷多个素数．
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| 关 键 词： | Fermat小定理 Diriehlet定理 Mobius反演公式 分圆多项式 素数 |
Generalization of Fermat little theorem and its application |
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| Zhang Min , Li Jinjiang , Ju Tengxia. Generalization of Fermat little theorem and its application[J]. Journal of Xuzhou Normal University(Natural Science Edition), 2012, 30(4): 1-5 |
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| Authors: | Zhang Min Li Jinjiang Ju Tengxia |
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| Affiliation: | (Department of Mathematics,College of Sciences,Nantong University,Nantong 226007,Jiangsu,China) |
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| Abstract: | In this paper, the Fermat little theorem is generalized from the integer ring Z to an ordinary set S using the methods of the fixed point and its order of a map. Aapplying this generalization, the Dirichlet theorem is dis- cussed and an elementary proof is given to show that whenever m≥3, then there exit infinite primes in sequence 1 ＋ lm（l= 0,1,2,%……）, which is a special case of the Diriehlet theorem. |
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| Keywords: | Fermat little theorem Dirichlet theorem Mobius inverse formula cyclotomic polynomial prime number |
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