Continued fraction factorization: Difference between revisions
Jump to navigation
Jump to search
imported>Citation bot Removed parameters. | Use this bot. Report bugs. | Suggested by Whoop whoop pull up | Category:Integer factorization algorithms | #UCB_Category 17/26 |
imported>OAbot m Open access bot: url-access=subscription updated in citation with #oabot. |
||
| Line 1: | Line 1: | ||
In [[number theory]], the '''continued fraction factorization method''' ('''CFRAC''') is an [[integer factorization]] [[algorithm]]. It is a general-purpose algorithm, meaning that it is suitable for factoring any integer ''n'', not depending on special form or properties. It was described by [[Derrick Henry Lehmer|D. H. Lehmer]] and [[R. E. Powers]] in 1931,<ref>{{cite journal|last = Lehmer|first = D.H.|author2=Powers, R.E.|title = On Factoring Large Numbers|journal = Bulletin of the American Mathematical Society|volume = 37|year = 1931|issue = 10|pages = 770–776|doi = 10.1090/S0002-9904-1931-05271-X|doi-access = free}}</ref> and developed as a computer algorithm by Michael A. Morrison and [[John Brillhart]] in 1975.<ref>{{cite journal|last = Morrison|first = Michael A.|author2=Brillhart, John|title = A Method of Factoring and the Factorization of ''F''<sub>7</sub>|journal = Mathematics of Computation|url = https://www.ams.org/journals/mcom/1975-29-129/S0025-5718-1975-0371800-5/|volume = 29|issue = 129| pages = 183–205|date=January 1975|doi = 10.2307/2005475|jstor = 2005475|publisher = American Mathematical Society}}</ref> | In [[number theory]], the '''continued fraction factorization method''' ('''CFRAC''') is an [[integer factorization]] [[algorithm]]. It is a general-purpose algorithm, meaning that it is suitable for factoring any integer ''n'', not depending on special form or properties. It was described by [[Derrick Henry Lehmer|D. H. Lehmer]] and [[R. E. Powers]] in 1931,<ref>{{cite journal|last = Lehmer|first = D.H.|author2=Powers, R.E.|title = On Factoring Large Numbers|journal = Bulletin of the American Mathematical Society|volume = 37|year = 1931|issue = 10|pages = 770–776|doi = 10.1090/S0002-9904-1931-05271-X|doi-access = free}}</ref> and developed as a computer algorithm by Michael A. Morrison and [[John Brillhart]] in 1975.<ref>{{cite journal|last = Morrison|first = Michael A.|author2=Brillhart, John|title = A Method of Factoring and the Factorization of ''F''<sub>7</sub>|journal = Mathematics of Computation|url = https://www.ams.org/journals/mcom/1975-29-129/S0025-5718-1975-0371800-5/|volume = 29|issue = 129| pages = 183–205|date=January 1975|doi = 10.2307/2005475|jstor = 2005475|publisher = American Mathematical Society|url-access = subscription}}</ref> | ||
The continued fraction method is based on [[Dixon's factorization method]]. It uses [[Convergent (continued fraction)|convergents]] in the [[continued fraction|regular continued fraction expansion]] of | The continued fraction method is based on [[Dixon's factorization method]]. It uses [[Convergent (continued fraction)|convergents]] in the [[continued fraction|regular continued fraction expansion]] of | ||
Latest revision as of 15:18, 24 June 2025
In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning that it is suitable for factoring any integer n, not depending on special form or properties. It was described by D. H. Lehmer and R. E. Powers in 1931,[1] and developed as a computer algorithm by Michael A. Morrison and John Brillhart in 1975.[2]
The continued fraction method is based on Dixon's factorization method. It uses convergents in the regular continued fraction expansion of
- .
Since this is a quadratic irrational, the continued fraction must be periodic (unless n is square, in which case the factorization is obvious).
It has a time complexity of , in the O and L notations.[3]
References
Further reading
- Script error: No such module "citation/CS1".