Un polynôme 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 Il n’y a pas de polynômes parfaits impairs ayant facteurs irréductibles. Il n’y a pas non plus de polynômes parfaits impairs ayant au plus facteurs irréductibles dans le cas où tous les exposants sont égaux à
A perfect polynomial over is a polynomial that equals the sum of all its divisors. If then we say that 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
@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}, pages = {165--174}, publisher = {Universit\'e Bordeaux 1}, volume = {19}, number = {1}, year = {2007}, doi = {10.5802/jtnb.579}, zbl = {1145.11081}, mrnumber = {2332059}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.579/} }
Luis H. Gallardo; Olivier Rahavandrainy. Odd perfect polynomials over ${\mathbb{F}_2}$. Journal de Théorie des Nombres de Bordeaux, Tome 19 (2007) no. 1, pp. 165-174. doi : 10.5802/jtnb.579. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.579/
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