System and method for finding integer solutions

Abstract

A system and a method for finding integer solutions of equations whose graphs are conic sections. The system provides a physical implementation of a geometric formulation of integer solutions of conic sections. The system includes a first source of waves and an arrangement of a plurality of reflectors to provide a lattice of interference patterns of standing waves in a plane, the lattice representing intersections at integer values. The system also includes a second source of waves and a detector provided along a curve that, with the second source, defines a cone of waves, which intersects with the plane of the lattice to provide a conic section. The detector finds points of intersection of the lattice and the conic section to determine integer solutions of the conic section. The conic section may be y=N/x, in which case the integer solutions provide a factorization into integers of N.

Dependencies are inferred from the claim text.