论文标题

关于具有限制性主要因素的整数集的添加和乘法分解,ii。 (平滑的数字和概括。)

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

论文作者

Gyory, K., Hajdu, L., Sarkozy, A.

论文摘要

在本文的第一部分中,我们研究了$ y $ -smooth数字的集合$ \ f_y $的加性可分解性,以及移位的乘积分解性$ \ g_y = \ f_y+\ f_y+\ {1 \} $。在本文中,关注“大型”功能$ y $的情况,我们继续研究这些问题。此外,我们还调查了与任意$ k $的$ k $ term总和的M-可解销性有关的问题。

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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