1Department of Mathematics, University of Brest 6 2Mathematics, University of Brest, 6, Avenue Le Gorgeu, C.S. 93837, 29238 Brest Cedex 3
Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 1, pp. 93-112
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Luis H. Gallardo; O. Rahavandrainy; Luis H. Gallardo; O. Rahavandrainy. Perfect polynomials over F_p with p+1 irreducible divisors. Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 1, pp. 93-112. http://geodesic.mathdoc.fr/item/AMUC_2014_83_1_a7/
@article{AMUC_2014_83_1_a7,
author = {Luis H. Gallardo and O. Rahavandrainy and Luis H. Gallardo and O. Rahavandrainy},
title = { Perfect polynomials over {F_p} with p+1 irreducible divisors},
journal = {Acta mathematica Universitatis Comenianae},
pages = {93--112},
year = {2014},
volume = {83},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2014_83_1_a7/}
}
TY - JOUR
AU - Luis H. Gallardo
AU - O. Rahavandrainy
AU - Luis H. Gallardo
AU - O. Rahavandrainy
TI - Perfect polynomials over F_p with p+1 irreducible divisors
JO - Acta mathematica Universitatis Comenianae
PY - 2014
SP - 93
EP - 112
VL - 83
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2014_83_1_a7/
ID - AMUC_2014_83_1_a7
ER -
%0 Journal Article
%A Luis H. Gallardo
%A O. Rahavandrainy
%A Luis H. Gallardo
%A O. Rahavandrainy
%T Perfect polynomials over F_p with p+1 irreducible divisors
%J Acta mathematica Universitatis Comenianae
%D 2014
%P 93-112
%V 83
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2014_83_1_a7/
%F AMUC_2014_83_1_a7
We consider, for a fixed prime number $p$, monic polynomials in one variable over the nite eld $F_p$, 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 rst unknown case, namely, the case $p = 3$.
