| Title:
|
Polynomials with values which are powers of integers (English) |
| Author:
|
Boumahdi, Rachid |
| Author:
|
Larone, Jesse |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
119-125 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $P$ be a polynomial with integral coefficients. Shapiro showed that if the values of $P$ at infinitely many blocks of consecutive integers are of the form $Q(m)$, where $Q$ is a polynomial with integral coefficients, then $P(x)=Q( R(x))$ for some polynomial $R$. In this paper, we show that if the values of $P$ at finitely many blocks of consecutive integers, each greater than a provided bound, are of the form $m^q$ where $q$ is an integer greater than 1, then $P(x)=( R(x))^q$ for some polynomial $R(x)$. (English) |
| Keyword:
|
integer-valued polynomial |
| MSC:
|
13F20 |
| idZBL:
|
Zbl 06890309 |
| idMR:
|
MR3813739 |
| DOI:
|
10.5817/AM2018-2-119 |
| . |
| Date available:
|
2018-06-05T14:17:59Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147218 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
