Detecting perfect powers in essentially linear time

被引：26

作者：

Bernstein, DJ ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

MATHEMATICS OF COMPUTATION | 1998年 / 67卷 / 223期

关键词：

D O I：

10.1090/S0025-5718-98-00952-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper (1) gives complete details of an algorithm to compute approximate kth roots; (2) uses this in an algorithm that, given an integer n > 1, either writes n as a perfect power or proves that n is not a perfect power; (3) proves, using Loxton's theorem on multiple linear forms in logarithms, that this perfect-power decomposition algorithm runs in time (log n)(1+o(1)).

引用

页码：1253 / 1283

页数：31

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