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Preprint . 2011
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The equation $\omega(n)=\omega(n+1)$

The equation \(\omega(n)=\omega(n+1)\)
descriptionPublicationkeyboard_double_arrow_right Preprint , Article 09 May 2011Publisher:John Wiley \& Sons, Chichester; London Mathematical Society, London
Authors: Schlage-Puchta, J.-C.;

arXiv: 1105.1621

The equation $\omega(n)=\omega(n+1)$

Abstract

Comment: The result is no obsolete: Buttkewitz found a non-computational proof, and the Goldston-Pintz-Yildirim-sieve yields more precise information

We prove that there are infinitely many integers $n$ such that $n$ and $n+1$ have the same number of distinct prime divisors.

Keywords

11N37, number of distinct prime factors, Mathematics - Number Theory, Asymptotic results on arithmetic functions

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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