Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(2): 513-524

Printed March 31, 2015

https://doi.org/10.4134/BKMS.2015.52.2.513

Copyright © The Korean Mathematical Society.

On the equation $\phi(5^m-1)=5^n-1$

Bernadette Faye, Florian Luca, and Amadou Tall

Km 2 route de Joal (Centre IRD Mbour), University of the Witwatersrand, Km 2 route de Joal (Centre IRD Mbour)

Abstract

Here, we show that the title equation has no positive integer solutions $(m,n)$, where $\phi$ is the Euler function.

Keywords: Diophantine equations, applications of primitive divisors, applications of sieve methods

MSC numbers: 11D61