On perfect polynomials over with irreducible factors

  • Luis H. Gallardo

    Université de Brest, France
  • Olivier Rahavandrainy

    Université de Brest, France


We consider, for a fixed odd prime number , monic polynomials in one variable over the finite field which are equal to the sum of their monic divisors. Call them \emph{perfect} polynomials. We prove that the exponents of each irreducible factor of any perfect polynomial having no root in and irreducible factors are all less than . We completely characterize those perfect polynomials for which each irreducible factor has degree two and all exponents do not exceed two.

Cite this article

Luis H. Gallardo, Olivier Rahavandrainy, On perfect polynomials over with irreducible factors. Port. Math. 69 (2012), no. 4, pp. 283–303

DOI 10.4171/PM/1918