Douglas Iannucci, University of Virgin Islands

Abstract

Hermite and Serret in 1848 independently devised an algorithm by which to find the two squares which add up to a given prime p of the form 4x+1. It works as well if p is composite. We generalize this algorithm to find representations of a natural number n as a binary quadratic form u2 + kuv + v2 for integers k ≥ 0 .