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

K. Gyory; L. Hajdu; A. Sarkozy

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arXiv · 2011.13008

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

K. Gyory·L. Hajdu·A. Sarkozy

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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 $k$.

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K. Gyory, L. Hajdu, A. Sarkozy. 2020-11-25. On additive and multiplicative decompositions of sets of integers with restricted prime factors, II. (Smooth numbers and generalizations.). https://arxiv.org/abs/2011.13008

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