Chowla定理的映射等价形式及其证明  

Mapping Equivalent Form of Chowla’s Theorem and Its Proof

作　　者：彭逢秋 漆林 崔世博 高莹 PENG Fengqiu;QI Lin;CUI Shibo;GAO Ying(Shenyuan College,Beihang University,Beijing 100191,China;School of Cyber Science and Technology,Beihang University,Beijing 100191,China;Zhongguancun Laboratory,Beijing 100094,China)

机构地区：[1]北京航空航天大学沈元学院,北京100191 [2]北京航空航天大学网络空间安全学院,北京100191 [3]中关村实验室,北京100094

出　　处：《大学数学》2025年第1期106-109,共4页College Mathematics

摘　　要：从映射的角度给出Chowla定理的等价表述形式,并推出该映射在定义域的某些特殊子集上构成其到自身的双射.进而利用Wilson定理在一般情形下的推广形式,分别通过反证法和数学归纳法两种思路推出矛盾,从而完成Chowla定理的映射等价形式的证明.From the point of view of mapping,the equivalent expression of Chowla theorem is given,and it is deduced that the mapping forms its bijection to itself on some special subsets of the definition domain.Then,by using the generalized form of Wilson’s theorem in general cases,the contradiction is deduced through two ideas,namely,the counter-proof method and the mathematical induction method,so as to complete the proof of the mapping equivalent form of Chowla’s theorem.

关 键 词：完全剩余系 WILSON定理 Chowla定理 

分 类 号：O156.1[理学—数学]