| 一个推广的Lucas型素性测定算法 |
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| 引用本文： | 周伟平.一个推广的Lucas型素性测定算法[J].安庆师范学院学报(自然科学版),2008,14(3). |
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| 作者姓名： | 周伟平 |
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| 作者单位： | 安庆师范学院,数学与计算科学学院,安徽,安庆,246133 |
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| 摘 要： | 特殊形式的自然数,例如形式为Mh,n=h.2n±1的数(h奇数,n正整数)常是人们感兴趣的研究对象。Berrizbeitia和Berry提出一个Lucass型素性测定测试,即当h mod 5时测试Mh,n的素性所用的种子仅依赖于h。本文推广了Berrizbeitia和Berry关于Mh,n=h.2n±1的素性测定,即将h不能被5整除推广到h不能被形如4m+1的素数q整除时的情形(特别当h能被15整除时)。
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| 关 键 词： | Lucas型素性测定算法 Lucas序列 四次剩余特征 本原不可约元 |
A Generalized Lucasian Primality Test |
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| ZHOU Wei-ping.A Generalized Lucasian Primality Test[J].Journal of Anqing Teachers College(Natural Science Edition),2008,14(3). |
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| Authors: | ZHOU Wei-ping |
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| Institution: | ZHOU Wei-ping(School of Mathematics , Computation Science,Anqing teachers College,Anqing 246133,China) |
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| Abstract: | Numbers of special form,such as Mh,n=h·2n±1(h,n positive integers with hodd),are often interested by mathematicians.Berrizbeitia and Berry present a test which allows one to test primality of Mh,n=h·2n±1 by means of a Lucasian sequence with a seed determined only by h,hmod 5.We present a primality test of the form Mh,n=h·2n-1(in particular with hdivisible by 15),which generalizes Berrizbeitia and Berry's test for such numbers with h≠0 mod 5. |
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| Keywords: | Lucasian primality test lucas sequence bi-quadratic residue characters primary irreducibles |
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