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- Title
ON AN INVERSE TERNARY GOLDBACH PROBLEM.
- Authors
XUANCHENG SHAO
- Abstract
We prove an inverse ternary Goldbach-type result. Let N be sufficiently large and c >0 be sufficiently small. If A1,A2,A3 ⊂[N] are subsets with |A1|, |A2|, |A3|≥N1/3-c, then A1+A2+A3 contains a composite number. This improves on the bound N1/3+o(1) obtained by using Gallagher's larger sieve. The main ingredients in our argument include a type of inverse sieve result in the larger sieve regime, and a variant of the analytic large sieve inequality.
- Subjects
GOLDBACH conjecture; COMPOSITE numbers; MATHEMATICAL bounds; SIEVES (Mathematics); MATHEMATICAL equivalence
- Publication
American Journal of Mathematics, 2016, Vol 138, Issue 5, p1167
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.2016.0038