Additive decompositions of sets with restricted prime factors

Elsholtz, Christian; Harper, Adam

doi:10.1090/S0002-9947-2014-06384-8

Additive decompositions of sets with restricted prime factors

Authors: Christian Elsholtz and Adam J. Harper
Journal: Trans. Amer. Math. Soc. 367 (2015), 7403-7427
MSC (2010): Primary 11N25, 11N36, 11P70
DOI: https://doi.org/10.1090/S0002-9947-2014-06384-8
Published electronically: November 4, 2014
MathSciNet review: 3378834
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Abstract: We investigate sumset decompositions of quite general sets with restricted prime factors. We manage to handle certain sets, such as the smooth numbers, even though they have little sieve amenability, and conclude that these sets cannot be written as a ternary sumset. This proves a conjecture by Sárközy. We also clean up and sharpen existing results on sumset decompositions of the prime numbers.

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