Cantor polynomials and the Fueter-Polya theorem

Abstract

A packing polynomial is a polynomial that maps the set $\mathbf{N}_0^2$ of lattice points with nonnegative coordinates bijectively onto $\mathbf{N}_0$. Cantor constructed two quadratic packing polynomials, and Fueter and Polya 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-Polya theorem. It is a century-old conjecture that t