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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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.
KeywordsChen’s theorem Estermann’s theorem Sieve method
Mathematics Subject Classification11P32 11N36 11N80
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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