| 关于等差数列型素数集的分解 |
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| 引用本文： | 石莹,严晓辉.关于等差数列型素数集的分解[J].数学的实践与认识,2017(11):277-281. |
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| 作者姓名： | 石莹 严晓辉 |
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| 作者单位： | 1. 南京中医药大学信息技术学院,江苏南京,210023;2. 南京师范大学数学科学学院,江苏南京,210023 |
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| 基金项目： | 国家自然科学基金资助课题(11471017) |
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| 摘 要： | 设C为非负整数集.若存在非负整数集A和B,使得C=A+B,其中|A|,|B|≥2,则称C为可分解的,否则称C为不可分解的或本原的.讨论特殊的等差数列型素数集合,证明了4k+1型素数集不可分解,以及4k+3型素数集不可分解.
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| 关 键 词： | 素数 可分解 本原 |
On Additive Decompositions of the Set Arithmetic Sequence of Prime |
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| SHI Ying,YAN Xiao-hui.On Additive Decompositions of the Set Arithmetic Sequence of Prime[J].Mathematics in Practice and Theory,2017(11):277-281. |
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| Authors: | SHI Ying YAN Xiao-hui |
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| Abstract: | If C is a finite or infinite set of non-negative integers,then it is said to be reducible if there are sets 4,B of non-negative integers withC =A + B and |A|,|B| ≥ 2.If there are no sets A,B with these properties,then C is said to be primitive.In this paper,it is proved that the sets of primes of 4k + 1 and 4k + 3 are both primitive. |
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| Keywords: | prime reducible primitive |
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