On the additive completion of primes

@article{Ruzsa1998OnTA,
  title={On the additive completion of primes},
  author={Imre Z. Ruzsa},
  journal={Acta Arithmetica},
  year={1998},
  volume={86},
  pages={269-275}
}
  • I. Ruzsa
  • Published 1998
  • Mathematics
  • Acta Arithmetica
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Note on the additive complements of primes
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  • V. Vu
  • Mathematics, Computer Science
  • 2002
We show that there is a set X ⊂ N with density O(log n) such that every sufficiently large natural number can be represented as sum of two elements from X and a prime. The density is a log n factor…
HIGH ORDER COMPLEMENTARY BASES OF PRIMES
  • V. Vu
  • Mathematics, Computer Science
  • 2002
We show that there is a set X ⊂ N with density O(log n) such that every sufficiently large natural number can be represented as sum of two elements from X and a prime. The density is a log n factor…

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Abstract In 1954 Lorentz and Erdos showed that there are very thin sets of positive integers complementary to the set of primes. In particular, there is anA⊆ N with[formula]and[formula]Erdos…
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Let 0 <a 1 <a2< . . . be any infinite sequence of integers . Denote by N(ai , n) the number of ai S n . I conjectured that to every sequence ai there corresponds a sequence b ; of density 0 (i .e .,…
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1. We prove that there is a set of nonnegative integers A, with counting function A(x) = #(A \ 1; x]) satisfying A(x) C log x loglogx; C a positive constant; such that N = (A + P) E, with N and…
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