| 关于分圆多项式系数的注记 |
| |
| 引用本文： | 钟祥贵.关于分圆多项式系数的注记[J].数学的实践与认识,2009,39(11). |
| |
| 作者姓名： | 钟祥贵 |
| |
| 作者单位： | 广西师范大学数学科学学院,广四,桂林,541004 |
| |
| 摘 要： | 自然数m称为HΓ数,如果分圆多项式Fm(x)的系数只能是0或±1.本文研究自然数m成为HΓ数的条件,证明:如果p是素数,那么1)m=15p(p>5)为HΓ数的充分必要条件是p≡±1(mod30);2)m=21p(p>7)为HΓ数的充分必要条件是p≡±1,±11,±19(mod42);3)m=33p(p>11)为HΓ数的充分必要条件是p≡±1,±7,±25(mod66).
|
| 关 键 词： | 分圆多项式 素数 同余 |
A Note on the Values of the Coefficients of a Cyclotomic Polynomial |
| |
| ZHONG Xiang-gui.A Note on the Values of the Coefficients of a Cyclotomic Polynomial[J].Mathematics in Practice and Theory,2009,39(11). |
| |
| Authors: | ZHONG Xiang-gui |
| |
| Abstract: | An positive integer is called a HΓ-number if the minimal polynomial of m-th root of unity over rational numbers has coefficients 0 and ±1. In this paper we completely determine if m is a HΓ-number for m=15p(p>5),m=21p(p>7),m=33p(p>11) respectively, where p denotes a prime. |
| |
| Keywords: | cyclotomic polynomial prime number congruence |
| 本文献已被 万方数据 等数据库收录！ |
|
