There is no odd perfect polynomial over with four prime factors

  • Luis H. Gallardo

    Université de Brest, France
  • Olivier Rahavandrainy

    Université de Brest, France

Abstract

A perfect polynomial over the binary field is a polynomial that equals the sum of all its divisors. If then we say that is odd. It is believed that odd perfect polynomials do not exist. In this article we prove this for odd perfect polynomials with four prime divisors, i.e., polynomials of the form where are distinct irreducible polynomials of degree 1 over and are positive integers.

Cite this article

Luis H. Gallardo, Olivier Rahavandrainy, There is no odd perfect polynomial over with four prime factors. Port. Math. 66 (2009), no. 2, pp. 131–145

DOI 10.4171/PM/1836