IJPAM: Volume 52, No. 2 (2009)

EVEN PERFECT POLYNOMIALS OVER $\F_2$
WITH FOUR PRIME FACTORS

Luis H. Gallardo$^1$, Olivier Rahavandrainy$^2$
$^{1,2}$Department of Mathematics
University of Brest
U.M.R. 6205, CNRS
6, Avenue Le Gorgeu, C.S. 93837,
Brest Cedex 3, 29238, FRANCE
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.A perfect polynomial over the binary field $\F_2$ is a polynomial $A \in \F_2[x]$ that equals the sum of all its divisors. If $\gcd(A,x^2-x) \neq 1$ then we call $A$ even. The list of all even perfect polynomials over $\F_2$ with at most $3$ prime factors in known. The object of this paper is to give the list of all even perfect polynomials over $\F_2$ with four prime factors. These are all the known perfect polynomials with four prime factors over $\F_2$.

Received: March 29, 2009

AMS Subject Classification: 11T55, 11T06

Key Words and Phrases: sum of divisors, polynomials, finite fields, characteristic 2

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 2