| 费马数是合数的一个充要条件 |
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| 引用本文： | 管训贵.费马数是合数的一个充要条件[J].四川理工学院学报(自然科学版),2009,22(4):23-24. |
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| 作者姓名： | 管训贵 |
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| 作者单位： | 泰州师范高等专科学校,江苏,泰州,225300 |
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| 摘 要： | 文章运用数论中的一些简单结果,如(F_m,F_n)=1及F_n=2~(2~n)+1(n≥2)的素因数p具有形状p=2~(n+2)k+1,其中k为某正整数等,给出了费马数是合数的一个充要条件,并得到了F_5,F_6和F_7的素因数分解式。
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| 关 键 词： | 费马数 合数 充要条件 素因数分解式 |
A Sufficient and Necessary Condition of the Proposition that the Fermat Numbers are Composite |
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| GUAN Xun-gui.A Sufficient and Necessary Condition of the Proposition that the Fermat Numbers are Composite[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2009,22(4):23-24. |
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| Authors: | GUAN Xun-gui |
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| Institution: | Taizhou Normal College;Taizhou 225300;China |
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| Abstract: | In this paper,we give a sufficient and necessary condition of the proposition that the Fermat number are composite, by using the simple result among the number theory,for instance,(F_m,F_n)=1 and suppose that p is a prime divisor of F_n=2~(2n)+1(n≥2),then it is of the from p=2~(n+2)k+1,where k is a positive integer.We also obtain the prime factorization of F_5,F_6 and F_7. |
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| Keywords: | Fermat numbers composite sufficient and necessary conditions prime factorization |
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