## On additive and multiplicative decompositions of sets of integers composed from a given set of primes, I (Additive decompositions)

### Volume 202 / 2022

Acta Arithmetica 202 (2022), 29-42
MSC: 11P32, 11P70.
DOI: 10.4064/aa210309-14-6
Published online: 7 December 2021

#### Abstract

In earlier papers Elsholtz and Harper, and the authors of this paper studied additive and multiplicative decomposability of sets of integers with restricted prime factors. Here we sharpen some results of Elsholtz and Harper on the additive decomposability of such sets by extending them to sets composed from a given “thin” (finite or infinite) set of primes, and we also study the additive decomposability of sets composed from a “very dense” set of primes.