On the parallel generation of the residues for the continued fraction factoring algorithm
H. C. Williams, Marvin C. Wunderlich · Mathematics of Computation · 1987
In order to implement the continued fraction algorithm on a highly parallel computer, like the Massively Parallel Processor, it is necessary to be able to compute certain numbers which occur at widely-spaced intervals within the continued fraction expansion of N \sqrt N . where N is the number to be factored. In this paper several properties of the continued fraction expansion of a quadratic irrational are developed. These results are then applied to the development of a very simple algorithm for finding the widely-spaced numbers referred to above.