Proceedings of the Japan Academy, Series A, Mathematical Sciences

On a Lehmer problem concerning Euler's totient function

Aleksander Grytczuk and Marek Wójtowicz

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Abstract

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 79, Number 8 (2003), 136-138.

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116443716

Digital Object Identifier
doi:10.3792/pjaa.79.136

Mathematical Reviews number (MathSciNet)
MR2013094

Zentralblatt MATH identifier
1045.11005

Subjects
Primary: 11A25: Arithmetic functions; related numbers; inversion formulas

Keywords
Lehmer problem Euler totient function

Citation

Grytczuk, Aleksander; Wójtowicz, Marek. On a Lehmer problem concerning Euler's totient function. Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), no. 8, 136--138. doi:10.3792/pjaa.79.136. https://projecteuclid.org/euclid.pja/1116443716


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