| 模m二次剩余系之Wilson定理 |
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| 引用本文： | 熊洪斌. 模m二次剩余系之Wilson定理[J]. 江西科学, 2011, 29(2): 153-155 |
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| 作者姓名： | 熊洪斌 |
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| 作者单位： | 蚌埠学院数学物理系,安徽蚌埠,233000 |
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| 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。
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| 关 键 词： | 二次剩余系 Wilson定理 同余数 |
Wilson Theorem on Quadratic Residue System of Modulus m |
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| XIONG Hong-bin. Wilson Theorem on Quadratic Residue System of Modulus m[J]. Jiangxi Science, 2011, 29(2): 153-155 |
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| Authors: | XIONG Hong-bin |
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| Affiliation: | XIONG Hong-bin(Mathematics and Physics Department,Bengbu College,Anhui Bengbu 233000 PRC) |
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| Abstract: | 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. |
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| Keywords: | Quadratic residue system Wilson theorem Congruent number |
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