On additive and multiplicative decompositions of sets of integers with restricted prime factors, II. (Smooth numbers and generalizations.)

K. Gyory; L. Hajdu; A. Sarkozy

paper

On additive and multiplicative decompositions of sets of integers with restricted prime factors, II. (Smooth numbers and generalizations.)

arXiv:2011.13008

Abstract

In part I of this paper we studied additive decomposability of the set $\F_y$ of th $y$ -smooth numbers and the multiplicative decomposability of the shifted set $\g_y=\F_y+\{1\}$. In this paper, focusing on the case of 'large' functions $y$ , we continue the study of these problems. Further, we also investigate a problem related to the m-decomposability of $k$ -term sumsets, for arbitrary $k$ .