  In this partly expository paper, we discuss three results. (1) That the
two-sided continued fraction of the normalized square root (an important part
of the SQUFOF algorithm) has several very attractive properties - periodicity,
a symmetry point corresponding to a factorization of $N$, and so on. (2) The
infrastructure distance formula. (3) A method for parallelization of SQUFOF
that maintains its efficiency per procesor as the number of processors
increases, and thus is predicted to be useful for very large numbers of
processors. The first two are known (in one form or another), the third may be
new (at least the implementation in C using MPI is new).

Number Theory;History and Overview