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 On the equation $\phi(5^m-1)=5^n-1$ Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 513-524 https://doi.org/10.4134/BKMS.2015.52.2.513Published online March 31, 2015 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 Downloads: Full-text PDF