The completion of Euler's factoring formula
Richard Blecksmith, John D. Brillhart, Michael Decaro · Rocky Mountain Journal of Mathematics · 2013
In this paper we derive a formula for a nontrivial factorization of an odd, composite integer N that has been expressed in two different ways as mx 2 + ny 2 .This derivation is based on an approach that Euler used in a special case in 1778.We also modify this formula to handle the case when N is expressed in two different ways as mx 2 -ny 2 .This latter factorization, however, may sometimes be trivial.