Chebyshev polynomials and Pell equations over finite fields
Czechoslovak Mathematical Journal (2021)
- Volume: 71, Issue: 2, page 491-510
- ISSN: 0011-4642
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topCohen, Boaz. "Chebyshev polynomials and Pell equations over finite fields." Czechoslovak Mathematical Journal 71.2 (2021): 491-510. <http://eudml.org/doc/298083>.
@article{Cohen2021,
abstract = {We shall describe how to construct a fundamental solution for the Pell equation $x^2-my^2=1$ over finite fields of characteristic $p\ne 2$. 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 $x^2-my^2=n$.},
author = {Cohen, Boaz},
journal = {Czechoslovak Mathematical Journal},
keywords = {finite field; Chebyshev polynomial; Pell equation},
language = {eng},
number = {2},
pages = {491-510},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Chebyshev polynomials and Pell equations over finite fields},
url = {http://eudml.org/doc/298083},
volume = {71},
year = {2021},
}
TY - JOUR
AU - Cohen, Boaz
TI - Chebyshev polynomials and Pell equations over finite fields
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 491
EP - 510
AB - We shall describe how to construct a fundamental solution for the Pell equation $x^2-my^2=1$ over finite fields of characteristic $p\ne 2$. 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 $x^2-my^2=n$.
LA - eng
KW - finite field; Chebyshev polynomial; Pell equation
UR - http://eudml.org/doc/298083
ER -
References
top- Benjamin, A. T., Walton, D., 10.1080/0025570X.2009.11953605, Math. Mag. 82 (2009), 117-126. (2009) Zbl1223.33013MR2512595DOI10.1080/0025570X.2009.11953605
- Ireland, K., Rosen, M., 10.1007/978-1-4757-2103-4, Graduate Texts in Mathematics 84. Springer, New York (1990). (1990) Zbl0712.11001MR1070716DOI10.1007/978-1-4757-2103-4
- LeVeque, W. J., Topics in Number Theory. Vol I, Dover Publications, Mineola (2002). (2002) Zbl1009.11001MR1942365
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