模m二次剩余系之Wilson定理  

Wilson Theorem on Quadratic Residue System of Modulus m

作　　者：熊洪斌[1] 

机构地区：[1]蚌埠学院数学物理系,安徽蚌埠233000

出　　处：《江西科学》2011年第2期153-155,共3页Jiangxi Science

摘　　要：主要研究了模m二次剩余系之Wilson定理,研究表明,若模m有原根,-1为模m的二次剩余,则模m的二次剩余系全体元素之积modm的同余数为-1;若不然,则模m二次剩余系全体元素之积modm的同余数为1。且模m二次非剩余系全体元素之积与二次剩余系全体元素之积modm的同余数相反。若m无原根,则模m二次剩余系全体元素之积与二次非剩余系全体元素之积modm的同余数相等。Wilson Theorem on Quadratic Residue System of Modulus m has been studied in this paper.It shows that if the modulus m has primitive roots,and-1 is a quadratic residue of the modulus m,then the congruent number of the product of all the quadratic residues is-1,otherwise,the congruent number of the product of all the quadratic residues is 1,and the congruent numbers between the products of all the quadratic nonresidues and residues of the modulus m are contrary.If the modulus m has no primitive roots,the congruent numbers between the products of all the quadratic nonresidues and residues of the modulus m are equal to each other.

关 键 词：二次剩余系 WILSON定理 同余数 

分 类 号：O156[理学—数学]