On étudie l’ensemble de tous les diviseurs de dans l’ordre croissant, et l’on obtient une borne supérieure pour les écarts entre deux diviseurs consécutifs. Nous obtenons une borne inférieure pour la différence entre les deux diviseurs les plus proches de .
The set of all divisors of , ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest and obtain a lower bound on their distance.
@article{AIF_1993__43_3_569_0, author = {Berend, Daniel and Harmse, J. E.}, title = {Gaps between consecutive divisors of factorials}, journal = {Annales de l'Institut Fourier}, volume = {43}, year = {1993}, pages = {569-583}, doi = {10.5802/aif.1348}, mrnumber = {94k:11107}, zbl = {0790.11007}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1993__43_3_569_0} }
Berend, Daniel; Harmse, J. E. Gaps between consecutive divisors of factorials. Annales de l'Institut Fourier, Tome 43 (1993) pp. 569-583. doi : 10.5802/aif.1348. http://gdmltest.u-ga.fr/item/AIF_1993__43_3_569_0/
[1] On the equation P(x) = n! and a question of Erdös, J. of Number Theory, 42 (1992), 189-193. | MR 93e:11016 | Zbl 0762.11010
and ,[2] Some problems and results in number theory, Number Theory and Combinatorics, Japan 1984, World Scientific, Singapore, 1985, 65-87. | Zbl 0603.10001
,[3] Some problems and results on additive and multiplicative number theory, Analytic Number Theory, (Philadelphia, 1980), Springer-Verlag Lecture Notes, 899 (1981), 171-182. | Zbl 0472.10002
,[4] Some solved and unsolved problems of mine in number theory, Topics in Analytic Number Theory, University of Texas Press, Austin, 1985, 59-75. | MR 804242 | Zbl 0596.10001
,[5] Personal communication.
,[6] Divisors, Cambridge University Press, Cambridge, 1988. | MR 90a:11107 | Zbl 0653.10001
and ,[7] Substitution Dynamical Systems - Spectral Analysis, Springer-Verlag Lecture Notes, 1294, Berlin, 1987. | MR 89g:54094 | Zbl 0642.28013
,[8] Sur un problème extrémal en arithmétique, Ann. Inst. Fourier, Grenoble, 37-2 (1987), 1-18. | Numdam | Numdam | MR 88k:11004 | Zbl 0622.10030
,[9] Integers with consecutive divisors in small ratio, J. of Number Theory, 19 (1984), 233-238. | MR 86c:11003 | Zbl 0543.10031
,[10] Limit theorems for divisor distributions, Proc. Amer. Math. Soc., 95 (1985), 505-511. | MR 87i:11126 | Zbl 0609.10041
,[11] The distribution of divisors of N!, Acta Arith., 50 (1988), 203-209. | MR 89j:11082 | Zbl 0647.10038
,