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

2020/11/25 by Kálmán Győry, Lajos Hajdu, Gyory, K. +3
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Finite Group Theory Research

paper · pdf · doi:10.48550/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.

Related

• On additive and multiplicative decompositions of sets of integers with restricted prime factors, I. (Smooth numbers.)
• Additive decompositions of sets with restricted prime factors
• Sums and Products with Smooth Numbers
• Metric decomposability theorems on sets of integers
• Metric decomposability theorems on sets of integers