INFINITUDE OF ELLIPTIC CARMICHAEL NUMBERS
INFINITUDE OF ELLIPTIC CARMICHAEL NUMBERS
复制标题
椭圆卡迈克尔数的无穷大
DOI：
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发表时间：
2012
影响因子：
0.7
通讯作者：
Aaron Ekstrom
中科院分区：
文献类型：
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作者：
Aaron Ekstrom
1987年，Gordon在费马小定理的基础上给出了一个与我们所熟悉的检验类似的整数素数条件，但却是基于椭圆曲线的复乘法运算。假设（特殊）等差数列中最小素数的界上的一个标准猜想的弱形式，通过所有的椭圆曲线素数检验，证明了无穷多个合数同时存在。我们的结果比1999年第一作者的论文（在第三作者的指导下写的）和2010年Banks和第二作者写的关于卡迈克尔数的剩余类的论文更普遍。
Abstract In 1987, Gordon gave an integer primality condition similar to the familiar test based on Fermat’s little theorem, but based instead on the arithmetic of elliptic curves with complex multiplication. We prove the existence of infinitely many composite numbers simultaneously passing all elliptic curve primality tests assuming a weak form of a standard conjecture on the bound on the least prime in (special) arithmetic progressions. Our results are somewhat more general than both the 1999 dissertation of the first author (written under the direction of the third author) and a 2010 paper on Carmichael numbers in a residue class written by Banks and the second author.