| Title:
|
Sum and difference sets containing integer powers (English) |
| Author:
|
Yang, Quan-Hui |
| Author:
|
Wu, Jian-Dong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
787-793 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let $C$ be a subset of $\{0,1,\cdots ,n\}$. We prove that if $$ |C|>\begin {cases} \lfloor n/2 \rfloor +1 &\text {if $m$ is odd}, \\ m \ell /2 +\delta &\text {if $m$ is even},\\ \end {cases} $$ where $\lfloor x \rfloor $ denotes the largest integer less than or equal to $x$ and $\delta $ denotes the cardinality of even numbers in the interval $[0,\min \{r,m-2\}]$, then $C-C$ contains a power of $m$. We also show that these lower bounds are best possible. (English) |
| Keyword:
|
sum and difference set |
| Keyword:
|
integer power |
| MSC:
|
11B13 |
| MSC:
|
11B30 |
| idZBL:
|
Zbl 1265.11017 |
| idMR:
|
MR2984634 |
| DOI:
|
10.1007/s10587-012-0045-2 |
| . |
| Date available:
|
2012-11-10T21:17:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143025 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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