No CrossRef data available.
Article contents
SUMSETS CONTAINING A TERM OF A SEQUENCE
Published online by Cambridge University Press: 18 September 2023
Abstract
Let $S=\{s_{1}, s_{2}, \ldots \}$ be an unbounded sequence of positive integers with $s_{n+1}/s_{n}$ approaching $\alpha $ as $n\rightarrow \infty $ and let $\beta>\max (\alpha , 2)$. We show that for all sufficiently large positive integers l, if $A\subset [0, l]$ with $l\in A$, $\gcd A=1$ and $|A|\geq (2-{k}/{\lambda \beta })l/(\lambda +1)$, where $\lambda =\lceil {k}/{\beta }\rceil $, then $kA\cap S\neq \emptyset $ for $2<\beta \leq 3$ and $k\geq {2\beta }/{(\beta -2)}$ or for $\beta>3$ and $k\geq 3$.
Keywords
MSC classification
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11071033, 12371003) and the Top Talents Project of Anhui Department of Education (Grant No. gxbjZD05).