This paper (1) gives complete details of an algorithm to compute approximate k k th roots; (2) uses this in an algorithm that, given an integer n > 1 n>1 , either writes n n as a perfect power or proves that n 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 ) (\log n)^{1+o(1)} .
CITATION STYLE
Bernstein, D. (1998). Detecting perfect powers in essentially linear time. Mathematics of Computation, 67(223), 1253–1283. https://doi.org/10.1090/s0025-5718-98-00952-1
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