| Title:
|
Chebyshev polynomials and Pell equations over finite fields (English) |
| Author:
|
Cohen, Boaz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
491-510 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We shall describe how to construct a fundamental solution for the Pell equation $x^2-my^2=1$ over finite fields of characteristic $p\neq 2$. Especially, a complete description of the structure of these fundamental solutions will be given using Chebyshev polynomials. Furthermore, we shall describe the structure of the solutions of the general Pell equation $x^2-my^2=n$. (English) |
| Keyword:
|
finite field |
| Keyword:
|
Chebyshev polynomial |
| Keyword:
|
Pell equation |
| MSC:
|
11D09 |
| MSC:
|
11D79 |
| MSC:
|
11T99 |
| MSC:
|
12E10 |
| MSC:
|
12E20 |
| idZBL:
|
07361081 |
| idMR:
|
MR4263182 |
| DOI:
|
10.21136/CMJ.2020.0451-19 |
| . |
| Date available:
|
2021-05-20T13:45:09Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148917 |
| . |
| Reference:
|
[1] Benjamin, A. T., Walton, D.: Counting on Chebyshev polynomials.Math. Mag. 82 (2009), 117-126. Zbl 1223.33013, MR 2512595, 10.1080/0025570X.2009.11953605 |
| Reference:
|
[2] Ireland, K., Rosen, M.: A Classical Introduction to Modern Number Theory.Graduate Texts in Mathematics 84. Springer, New York (1990). Zbl 0712.11001, MR 1070716, 10.1007/978-1-4757-2103-4 |
| Reference:
|
[3] LeVeque, W. J.: Topics in Number Theory. Vol I.Dover Publications, Mineola (2002). Zbl 1009.11001, MR 1942365 |
| . |
