In number theory, the continued fraction factorization method is an integer factorizationalgorithm. 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.
Continuedfractions are motivated by a desire to have a "mathematically pure" representation for the real numbers.
The continuedfraction representations of a rational number and its reciprocal are identical except for a shift one place left or right depending on whether the number is less than or greater than one respectively.
Continuedfractions also play a role in the study of chaos, where they tie together the Farey fractions which are seen in the Mandelbrot set with Minkowski's question mark function and the modular group Gamma.
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