Abstract. 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 fÑ~, 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.

A number theory package is described which uses doubly linked list structures for storing multiprecise integers. The package has been coded in IBM's Basic Assembly Language and makes heavy use of the macro language and conditional assembly. An optimally coded trial division routine is also described which can be used to determine the unique factorization of large integers.

No abstract

Abstract. 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 fÑ~, 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.

No abstract