GENERALIZED CULLEN NUMBERS WITH THE LEHMER PROPERTY

Title & Authors
GENERALIZED CULLEN NUMBERS WITH THE LEHMER PROPERTY
Kim, Dae-June; Oh, Byeong-Kweon;

Abstract
We say a positive integer n satisfies the Lehmer property if $\small{{\phi}(n)}$ divides n - 1, where $\small{{\phi}(n)}$ is the Eulers totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfying the Lehmer property is known. In this article, we show that every composite integer of the form $D_{p,n} Keywords Eulers totient function;generalized Cullen number;Lehmer property; Language English Cited by 1. Pell numbers with the Lehmer property, Afrika Matematika, 2017, 28, 1-2, 291 References 1. J. Cilleruelo and F. Luca, Repunit Lehmer numbers, Proc. Edinb. Math. Soc. (2) 54 (2011), no. 1, 55-65. 2. G. L. Cohen and P. Hagis Jr., On the number of prime factors of n if${\phi}(n)|(n-1)\$, Nieuw.Arch. Wisk. (3) 28 (1980), no. 2, 177-185.

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