On donne une estimation expérimentale du taux moyen de croissance de la longueur de la période des progressions géométriques pour n croissant, pour des valeurs différentes de q. Les résultats empiriques, obtenus pour n jusqu'à 106, permettent de conjecturer que l'ordre moyen de la longueur de la période est , où la constante C dépend de q.
The averaged growth rate of period's length of the geometrical progressions for increasing n is empirically estimated for different values of q. The experimental results, obtained for n up to 106, allow us to conjecture that the average order of period's length is , where constant C depends on q.
@article{CRMATH_2004__339_1_15_0, author = {Francesca Aicardi}, title = {Empirical estimates of the average orders of orbits period lengths in {Euler} groups}, journal = {Comptes Rendus. Math\'ematique}, pages = {15--20}, publisher = {Elsevier}, volume = {339}, number = {1}, year = {2004}, doi = {10.1016/j.crma.2004.02.021}, language = {en}, }
Francesca Aicardi. Empirical estimates of the average orders of orbits period lengths in Euler groups. Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 15-20. doi : 10.1016/j.crma.2004.02.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.02.021/
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