ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE





Perfect polynomials over Fp with p + 1 irreducible divisors

L. H. Gallardo and O. Rahavandrainy

Received: March 3, 2013;   Accepted: September 16, 2013



Abstract.   We consider, for a fixed prime number p, monic polynomials in one variable over the finite field Fp, which are equal to the sum of their monic divisors. We give necessary conditions for the existence of such polynomials, called perfect polynomials, having p + 1 irreducible factors. These conditions allow us to describe the set of all perfect polynomials with p + 1 irreducible divisors in the first unknown case, namely, the case p = 3.

Keywords:  Sum of divisors; polynomials; finite fields; characteristic p.  

AMS Subject classification: Primary:  11T55, 11T06  


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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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