Generalized Cullen numbers with the Lehmer property
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We say a positive integer n satisfies the Lehmer property if Φ(n) divides n − 1, where Φ(n) is the Euler’s totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfy- ing the Lehmer property is known. In this article, we show that every composite integer of the form Dp,n = npn+1, for a prime p and a positive integer n, or of the form α2β + 1 for α≤ β does not satisfy the Lehmer property.
Abstract
We say a positive integer n satisfies the Lehmer property if Φ(n) divides n − 1, where Φ(n) is the Euler’s totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfy- ing the Lehmer property is known. In this article, we show that every composite integer of the form Dp,n = npn+1, for a prime p and a positive integer n, or of the form α2β + 1 for α≤ β does not satisfy the Lehmer property.
참고문헌 (6)
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