| 合数是绝对假素数的充要条件 |
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| 引用本文： | 袁新梅,李鹤年.合数是绝对假素数的充要条件[J].数学研究,2002,35(4):451-455. |
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| 作者姓名： | 袁新梅 李鹤年 |
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| 作者单位： | 江西宜春学院数学系,江西,宜春,336000 |
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| 摘 要： | 利用正整数模的特征数这一新概念给出了合数是绝对假素数的充要条件。以此为据，证明了绝对假素数是奇数，它无异于1的平方因数，并且至少是三个互异的奇素数的乘积；还给出了两个绝对假素数或两个大于1的奇数的乘积是绝对假素数的充要条件。
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| 关 键 词： | 合数 绝对假素数 充要条件 简化剩余系 二次剩余 正整数 标准分解式 |
| 修稿时间： | 2002年3月7日 |
The Necessary and Sufficient Condition for that a Composite Number is the Absolute False Prime Number |
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| Yuan Xinmei,Li Henian.The Necessary and Sufficient Condition for that a Composite Number is the Absolute False Prime Number[J].Journal of Mathematical Study,2002,35(4):451-455. |
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| Authors: | Yuan Xinmei Li Henian |
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| Abstract: | In this paper, we show a necessary and sufficient condition for that a composite number is the absolute false prime number by a new concept - the characteristic number of the modulus of a positive integer. According to this result, we prove that a absolute false prime number is odd, and it has no square factors besides 1 and it is the product of at least three distinct odd prime number. At the same time, we show a necessary and sufficient condition for that the product of two absolute false prime number or two odd number with both larger than 1 is absolute false prime. |
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| Keywords: | reduced residue system quadratic residue standard factorization of positive integer |
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