Displaying similar documents to “The 3rd Czech and Polish Conference on Number Theory. Problem session”

On the sumset of the primes and a linear recurrence

Christian Ballot, Florian Luca (2013)

Acta Arithmetica

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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.