On the sumset of the primes and a linear recurrence

• Autorzy: Christian Ballot , Florian Luca
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11B37: Recurrences
• 11P32: Goldbach-type theorems; other additive questions involving primes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 1
• Strony: 33-46

Daty

wydano

2013

Twórcy

autor

Christian Ballot

• L.M.N.O., CNRS UMR 6139, Université de Caen, F-14032 Caen Cedex, France

autor

Florian Luca

• Fundación Marcos Moshinsky, UNAM, Circuito Exterior, C.U., Apdo. Postal 70-543, México, D.F. 04510, México

Identyfikatory

DOI

10.4064/aa161-1-3