  In this paper, we will describe a new factorization algorithm based on the
continuous representation of Gauss sums, generalizable to orders j>2. Such an
algorithm allows one, for the first time, to find all the factors of a number N
in a single run without precalculating the ratio N/l, where l are all the
possible trial factors. Continuous truncated exponential sums turn out to be a
powerful tool for distinguishing factors from non-factors (we also suggest,
with regard to this topic, to read an interesting paper by S. Woelk et al. also
published in this issue [Woelk, Feiler, Schleich, J. Mod. Opt. in press]) and
factorizing different numbers at the same time. We will also describe two
possible M-path optical interferometers, which can be used to experimentally
realize this algorithm: a liquid crystal grating and a generalized symmetric
Michelson interferometer.
