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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a conjecture of Balog


Author: Adolf Hildebrand
Journal: Proc. Amer. Math. Soc. 95 (1985), 517-523
MSC: Primary 11A05; Secondary 11B05
MathSciNet review: 810155
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Abstract: A conjecture of A. Balog is proved which gives a sufficient condition on a set $ A$ of positive integers such that $ A \cap (A + 1)$ is infinite. A consequence of this result is that, for every $ \varepsilon > 0$, there are infinitely many integers $ n$ such that both $ n$ and $ n + 1$ have a prime factor $ > {n^{1 - \varepsilon }}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0810155-4
PII: S 0002-9939(1985)0810155-4
Article copyright: © Copyright 1985 American Mathematical Society