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 Euler's 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 $\small{D_{p,n}=np^n+1}$, for a prime p and a positive integer n, or of the form $\small{{\alpha}2^{\beta}+1}$ for $\small{{\alpha}{\leq}{\beta}}$ does not satisfy the Lehmer property.
Keywords
Euler's 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
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