Perfect polynomials over
F_{p} with p + 1 irreducible divisorsL. 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 F_{p}, 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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