منابع مشابه
Repunit Lehmer numbers
A Lehmer number is a composite positive integer n such that φ(n) | n− 1. In this paper, we show that given a positive integer g > 1 there are at most finitely many Lehmer numbers which are repunits in base g, and they are all effectively computable. Our method is effective and we illustrate it by showing that there is no such Lehmer number when g ∈ [2, 1000]. 2000 Mathematics Subject Classifica...
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Here, we show that there is no positive integer n such that the nth Cullen number Cn = n2n + 1 has the property that it is composite but φ(Cn) | Cn − 1.
متن کاملThe Multiplicative Group Generated by the Lehmer Numbers
That is, U is the range of the sequence (un)n>o. In this paper, we look at the set G(u) D N . Certainly, U C G(u) D N C N . It is easy to see that the extreme cases of the above inclusions can occur in some non-trivial instances. For example, if un = n\ for all n > 0, then m = um/um-i for all ra > 1, therefore G(u) = N . However, if (un)n>o is an arithmetical progression of first term 1 and dif...
متن کاملNew Pseudorandom Sequences Constructed by Quadratic Residues and Lehmer Numbers
Let p be an odd prime. Define en = { (−1), if n is a quadratic residue mod p, (−1)n+n+1, if n is a quadratic nonresidue mod p, where n is the multiplicative inverse of n modulo p such that 1 ≤ n ≤ p − 1. This paper shows that the sequence {en} is a “good” pseudorandom sequence, by using the properties of exponential sums, character sums, Kloosterman sums and mean value theorems of Dirichlet L-f...
متن کاملExistence of Primitive Divisors of Lucas and Lehmer Numbers
We prove that for n > 30, every n-th Lucas and Lehmer number has a primitive divisor. This allows us to list all Lucas and Lehmer numbers without a primitive divisor. Whether the mathematicians like it or not, the computer is here to stay. Folklore Whether the computer likes it or not, mathematics is here to stay. Beno Eckmann 32], p. xxiii Contents 1 Introduction 1 2 Cyclotomic criterion and n...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1993
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-66-1-85-93