Cantor Polynomials and the Fueter-Pólya Theorem. Issue 10 (1st December 2016) - Nathanson, Melvyn B.
Abstract: A packing polynomial is a polynomial that maps the set N 2 0 of lattice points with nonnegative coordinates bijectively onto N0 . Cantor constructed two quadratic packing polynomials, and Fueter and Pólya proved analytically that the Cantor polynomials are the only quadratic packing polynomials. The purpose of this paper is to present a beautiful elementary proof of Vsemirnov of the Fueter–Pólya theorem. It is a century-old conjecture that the Cantor polynomials are the only packing polynomials on N 2 0 .