关于等差数列型素数集的分解  

On Additive Decompositions of the Set Arithmetic Sequence of Prime

作　　者：石莹[1] 严晓辉[2] 

机构地区：[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

出　　处：《数学的实践与认识》2017年第11期277-281,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金资助课题(11471017)

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.If C is a finite or infinite set of non-negative integers, then it is said to be reducibleif there are sets ,4, B of non-negative integers with C -- A ＋ B and },41, IBI 〉 2. If there areno sets ,4, B with these properties, then C is said to be primitive. In this paper, it is provedthat the sets of primes of 4k ＋ 1 and 4k ＋ 3 are both primitive.

关 键 词：素数 可分解 本原 

分 类 号：O156[理学—数学]