On a Lehmer problem concerning Euler's totient function

Grytczuk, Aleksander; Wójtowicz, Marek

Proc. Japan Acad. Ser. A Math. Sci., Tome 79 (2003) no. 3, p. 136-138 / Harvested from Project Euclid

Résumé

Let $M$ be a positive integer with $M > 4$, and let $\varphi$ denote Euler's totient function. If a positive integer $n$ satisfies the Diophantine equation (*) $M \varphi(n) = n - 1$, then the number of prime factors of $n$ is much bigger than $M$. Moreover, the set of all squarefree integers which do not fulfil (*) contains ``nice'' subsets.

Publié le : 2003-10-14
Classification: Lehmer problem, Euler totient function, 11A25

@article{1116443716,
     author = {Grytczuk, Aleksander and W\'ojtowicz, Marek},
     title = {On a Lehmer problem concerning Euler's totient function},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {79},
     number = {3},
     year = {2003},
     pages = { 136-138},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116443716}
}

Grytczuk, Aleksander; Wójtowicz, Marek. On a Lehmer problem concerning Euler's totient function. Proc. Japan Acad. Ser. A Math. Sci., Tome 79 (2003) no. 3, pp.  136-138. http://gdmltest.u-ga.fr/item/1116443716/