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Continued fraction factorization

In number theory, the continued fraction factorization method 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 developed by Michael A. Morrison and John Brillhart in 1975.

The continued fraction method is based on Dixon's factorization method. It uses convergents in the continued fraction of

\sqrt{kn},\qquad k\in\mathbb{Z^+}.

Since this is a quadratic irrational, the continued fraction must be periodic (unless n is square, in which case the factorization is obvious).

01-04-2007 01:16:19
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