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The Ramanujan Journal
Article . 2024 . Peer-reviewed
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Preprint . 2022
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A generalization of Lehman’s method

A generalization of Lehman's method
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 28 Oct 2024Embargo end date: 01 Jan 2022 English Publisher:Springer Science and Business Media LLCJournal:The Ramanujan Journal, volume 65, pages 1,773-1,790 (issn: 1382-4090, eissn: 1572-9303, Copyright policy )
Authors: Hales, Jonathon; Hiary, Ghaith;

doi: 10.1007/s11139-024-00959-7 , 10.48550/arxiv.2209.15586

arXiv: http://arxiv.org/abs/2209.15586

A generalization of Lehman’s method

Abstract

AbstractA new deterministic algorithm for finding square divisors, and finding r-power divisors in general, is presented. This algorithm is based on Lehman’s method for integer factorization and is straightforward to implement. While the theoretical complexity of the new algorithm is far from best known, the algorithm becomes especially effective if even a loose bound on a square divisor is known. Additionally, we answer a question by D. Harvey and M. Hittmeir on whether their recent deterministic algorithm for integer factorization can be adapted to finding r-power divisors.

Related Organizations
Keywords

algorithm, Mathematics - Number Theory, square-free numbers, integer factorization, FOS: Mathematics, 11Y05, 11Y16, Number Theory (math.NT), Factorization, Factorization; primality, rational approximation, Number-theoretic algorithms; complexity

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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