Odd perfect polynomials over 𝔽 2
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Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 1, pp. 165-174.

A perfect polynomial over 𝔽 2 is a polynomial A𝔽 2 [x] that equals the sum of all its divisors. If gcd(A,x 2 +x)=1 then we say that A is odd. In this paper we show the non-existence of odd perfect polynomials with either three prime divisors or with at most nine prime divisors provided that all exponents are equal to 2.

Un polynôme A𝔽 2 [x] est dit parfait s’il est égal à la somme de tous ses diviseurs et il est dit impair s’il n’a pas de facteurs de degré 1. Il n’y a pas de polynômes parfaits impairs ayant 3 facteurs irréductibles. Il n’y a pas non plus de polynômes parfaits impairs ayant au plus 9 facteurs irréductibles dans le cas où tous les exposants sont égaux à 2.

Received: 2005-11-13
Published online: 2008-12-03
DOI: https://doi.org/10.5802/jtnb.579
@article{JTNB_2007__19_1_165_0,
     author = {Luis H. Gallardo and Olivier Rahavandrainy},
     title = {Odd perfect polynomials over ${\mathbb{F}\_2}$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {19},
     number = {1},
     year = {2007},
     pages = {165-174},
     doi = {10.5802/jtnb.579},
     zbl = {1145.11081},
     mrnumber = {2332059},
     language = {en},
     url={jtnb.centre-mersenne.org/item/JTNB_2007__19_1_165_0/}
}
Gallardo, Luis H.; Rahavandrainy, Olivier. Odd perfect polynomials over ${\mathbb{F}_2}$. Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 1, pp. 165-174. doi : 10.5802/jtnb.579. https://jtnb.centre-mersenne.org/item/JTNB_2007__19_1_165_0/

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