Finiteness of Ulam Polynomials

TL;DR

This paper proves that for each polynomial degree, there are only finitely many Ulam polynomials, which have coefficients equal to their roots, establishing a key finiteness property.

Contribution

The paper establishes the finiteness of Ulam polynomials for each degree, a previously unresolved question in polynomial root-coefficient relationships.

Findings

Finite number of Ulam polynomials for each degree n

Proof of the finiteness property for Ulam polynomials

Advances understanding of polynomial root-coefficient structures

Abstract

A polynomial whose coeffcients are equal to its roots is called a Ulam polynomial. In this paper we show that for a given degree n there exists a finite number of Ulam polynomials of degree n.