On polynomials with only rational roots

Mathematika, vol. 69, pp. 867–878

Abstract

Abstract In this paper, we study upper bounds for the degrees of polynomials with only rational roots. First, we assume that the coefficients are bounded. In the second theorem, we suppose that the primes 2 and 3 do not divide any coefficient. The third theorem concerns the case that all coefficients are composed of primes from a fixed finite set.

Authors 3

1. Lajos Hajdu corresponding

   University of Debrecen

   Affiliation as printed

   ELKH‐DE Equations, Functions, Curves and their Applications Research Group Debrecen Hungary

   Institute of Mathematics University of Debrecen Debrecen Hungary

   ELKH-DE Equations, Functions, Curves and their Applications Research Group, Debrecen, Hungary

   Institute of Mathematics, University of Debrecen, Debrecen, Hungary

2. Rob Tijdeman Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute Leiden University Leiden The Netherlands

   Mathematical Institute, Leiden University, Leiden, The Netherlands

3. Nóra Varga

   University of Debrecen

   Affiliation as printed

   ELKH‐DE Equations, Functions, Curves and their Applications Research Group Debrecen Hungary

   Institute of Mathematics University of Debrecen Debrecen Hungary

   ELKH-DE Equations, Functions, Curves and their Applications Research Group, Debrecen, Hungary

   Institute of Mathematics, University of Debrecen, Debrecen, Hungary