On the representation of a large integer as the sum of a prime and a square-free number with at most three prime divisors

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Abstract

In this paper we prove that every sufficiently large odd integer can be written as a sum of a prime and 2 times a product of at most two distinct odd primes. Together with Chen’s theorem and Ross’s observation, this shows every sufficiently large integer can be written as a sum of a prime and a square-free number with at most three prime divisors.

Keywords

Chen’s theorem Estermann’s theorem Sieve method 

Mathematics Subject Classification

11P32 11N36 11N80 

Notes

Acknowledgements

The author is very grateful to Jim Brown, Luke Giberson, Kevin James, Daozhou Zhu and the reviewer for their helpful discussions and suggestions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesClemson UniversityClemsonUSA

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