On the sumset of the primes and a linear recurrence

Christian Ballot; Florian Luca

Displaying similar documents to “On the sumset of the primes and a linear recurrence”

The 3rd Czech and Polish Conference on Number Theory. Problem session

Štefan Porubský, Kazimierz Szymiczek (2000)

Acta Mathematica et Informatica Universitatis Ostraviensis

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On theorems of Niven and Dressler

Štefan Porubský (1978)

Mathematica Slovaca

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The Romanoff theorem revisited

Hongze Li, Hao Pan (2008)

Acta Arithmetica

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Nonaliquots and Robbins numbers

William D. Banks, Florian Luca (2005)

Colloquium Mathematicae

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Let φ(·) and σ(·) denote the Euler function and the sum of divisors function, respectively. We give a lower bound for the number of m ≤ x for which the equation m = σ(n) - n has no solution. We also show that the set of positive integers m not of the form (p-1)/2 - φ(p-1) for some prime number p has a positive lower asymptotic density.

Prime divisors of linear recurrences and Artin's primitive root conjecture for number fields

Hans Roskam (2001)

Journal de théorie des nombres de Bordeaux

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Let $S$ be a linear integer recurrent sequence of order $k \geq 3$ , and define $P_{S}$ as the set of primes that divide at least one term of $S$ . We give a heuristic approach to the problem whether $P_{S}$ has a natural density, and prove that part of our heuristics is correct. Under the assumption of a generalization of Artin’s primitive root conjecture, we find that $P_{S}$ has positive lower density for “generic” sequences $S$ . Some numerical examples are included.