How to Find Smooth Parts of Integers
نویسنده
چکیده
Let P be a finite set of primes, and let S be a finite sequence of positive integers. This paper presents an algorithm to find the largest P smooth divisor of each integer in S. The algorithm takes time b(lg b)2+o(1), where b is the total number of bits in P and S. A previous algorithm by the author takes time b(lg b)3+o(1) to find all the factors from P of each integer in S; a variant by Franke, Kleinjung, Morain, and Wirth usually takes time b(lg b)2+o(1) to find the largest P -smooth divisor of each integer in S; the algorithm in this paper always takes time b(lg b)2+o(1) to find the largest P smooth divisor of each integer in S.
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