Detecting perfect powers in essentially linear time

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).

• Type: Journal
• Year: 1998
• Where: MOC
• Authors: Daniel J. Bernstein
• Keywords: Algorithm, Kth Roots, MOC 1998, Perfect Power