# On the sumset of the primes and a linear recurrence

Christian Ballot; Florian Luca

Acta Arithmetica (2013)

- Volume: 161, Issue: 1, page 33-46
- ISSN: 0065-1036

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topChristian Ballot, and Florian Luca. "On the sumset of the primes and a linear recurrence." Acta Arithmetica 161.1 (2013): 33-46. <http://eudml.org/doc/286068>.

@article{ChristianBallot2013,

abstract = {Romanoff (1934) showed that integers that are the sum of a prime and a power of 2 have positive lower asymptotic density in the positive integers. We adapt his method by showing more generally the existence of a positive lower asymptotic density for integers that are the sum of a prime and a term of a given nonconstant nondegenerate integral linear recurrence with separable characteristic polynomial.},

author = {Christian Ballot, Florian Luca},

journal = {Acta Arithmetica},

keywords = {Goldbach-type theorems; linear recurrence; primes; sumsets; asymptotic density; S-units},

language = {eng},

number = {1},

pages = {33-46},

title = {On the sumset of the primes and a linear recurrence},

url = {http://eudml.org/doc/286068},

volume = {161},

year = {2013},

}

TY - JOUR

AU - Christian Ballot

AU - Florian Luca

TI - On the sumset of the primes and a linear recurrence

JO - Acta Arithmetica

PY - 2013

VL - 161

IS - 1

SP - 33

EP - 46

AB - Romanoff (1934) showed that integers that are the sum of a prime and a power of 2 have positive lower asymptotic density in the positive integers. We adapt his method by showing more generally the existence of a positive lower asymptotic density for integers that are the sum of a prime and a term of a given nonconstant nondegenerate integral linear recurrence with separable characteristic polynomial.

LA - eng

KW - Goldbach-type theorems; linear recurrence; primes; sumsets; asymptotic density; S-units

UR - http://eudml.org/doc/286068

ER -

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