Additive decompositions of sets with restricted prime factors

2013/09/03 by Elsholtz, Christian, Harper, Adam J. · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1309.0593

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.

Cited by

• An inverse theorem on sets with rich additive structure modulo primes

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• On additive and multiplicative decompositions of sets of integers with restricted prime factors, I. (Smooth numbers.)
• On additive and multiplicative decompositions of sets of integers with restricted prime factors, II. (Smooth numbers and generalizations.)
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• Problems 66 and 67 on sums of residue classes and primes of András Sárközy's collection of unsolved problems