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SUMSETS CONTAINING A TERM OF A SEQUENCE.
- Source :
-
Bulletin of the Australian Mathematical Society . Jun2024, Vol. 109 Issue 3, p420-428. 9p. - Publication Year :
- 2024
-
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 and $k\geq {2\beta }/{(\beta -2)}$ or for $\beta>3$ and $k\geq 3$. [ABSTRACT FROM AUTHOR]
- Subjects :
- *INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 00049727
- Volume :
- 109
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 177292592
- Full Text :
- https://doi.org/10.1017/S0004972723000904