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Comptes Rendus Mathématique
Volume 347, n° 19-20
pages 1111-1114 (octobre 2009)
Doi : 10.1016/j.crma.2009.07.019
Received : 21 July 2008 ;  accepted : 17 July 2009
Appendix to the Note “The structure of the set of numbers with the Lehmer property”
Appendice à l’article : « Structure de l’ensemble des entiers possèdant la propriété de Lehmer »
 

Marek Wójtowicz , Marta Skonieczna
Instytut Matematyki, Uniwersytet Kazimierza Wielkiego, Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland 

Abstract

Let denote the Euler totient function, and let P be a monic polynomial with integer coefficients and positive degree. Combining the techniques of proof from our previous paper and that of a recent paper by Hernández and Luca we generalize the following result of Hernández and Luca: the set of composite positive integers n such that   and   is finite. The generalization is of the quantitative type, and applies also to the so-called unitary analogue of the Lehmer problem (studied earlier by Subbarao and Siva Rama Prasad). To cite this article: M. Wójtowicz, M. Skonieczna, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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Résumé

Soit la fonction indicatrice d’Euler, et P un polynôme unitaire à coefficients entiers et de degré strictement positif. En combinant les techniques de démonstration de notre précédent article et celles d’un article récent de Hernández et Luca, nous généralisons le résultat suivant de Hernández et Luca : l’ensemble des entiers n strictement positifs composés tels que   et  , est fini. La généralisation est quantitative, et s’applique aussi à l’analogue unitaire du problème de Lehmer (antérieurement étudié par Subbarao et Siva Rama Prasad). Pour citer cet article : M. Wójtowicz, M. Skonieczna, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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