Continued fraction factorization

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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 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

.

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 complexity of O(exp(c(log n log log n))), where c is a constant.