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On a Problem of Erdös in Additive Number Theory

✍ Scribed by Dieter Wolke

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 263 KB
Volume: 59
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0094

No coin nor oath required. For personal study only.

✦ Synopsis

In 1954 Lorentz and Erdo s showed that there are very thin sets of positive integers complementary to the set of primes. In particular, there is an A N with

(ii) every n n 0 can be written as n=a+ p, a # A, p prime.

Erdo s conjectured that the bound (i) could be sharpened to o(ln 2 x) or even O(ln x). In the present paper it is proved that there are sets A with A(x)Rh(x) ln ln x } ln x (h tending to arbitrarily slowly) such that (ii) is fulfilled for almost all n.

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