Geodesic
Chebyshev polynomials and Pell equations over finite fields
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 491-510

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $x^2-my^2=n$.
DOI : 10.21136/CMJ.2020.0451-19
Classification : 11D09, 11D79, 11T99, 12E10, 12E20
Keywords: finite field; Chebyshev polynomial; Pell equation 
@article{10_21136_CMJ_2020_0451_19,
     author = {Cohen, Boaz},
     title = {Chebyshev polynomials and {Pell} equations over finite fields},
     journal = {Czechoslovak Mathematical Journal},
     pages = {491--510},
     publisher = {mathdoc},
     volume = {71},
     number = {2},
     year = {2021},
     doi = {10.21136/CMJ.2020.0451-19},
     mrnumber = {4263182},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0451-19/}
}
TY  - JOUR
AU  - Cohen, Boaz
TI  - Chebyshev polynomials and Pell equations over finite fields
JO  - Czechoslovak Mathematical Journal
PY  - 2021
SP  - 491
EP  - 510
VL  - 71
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0451-19/
DO  - 10.21136/CMJ.2020.0451-19
LA  - en
ID  - 10_21136_CMJ_2020_0451_19
ER  - 
%0 Journal Article
%A Cohen, Boaz
%T Chebyshev polynomials and Pell equations over finite fields
%J Czechoslovak Mathematical Journal
%D 2021
%P 491-510
%V 71
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0451-19/
%R 10.21136/CMJ.2020.0451-19
%G en
%F 10_21136_CMJ_2020_0451_19
Cohen, Boaz. Chebyshev polynomials and Pell equations over finite fields. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 491-510. doi: 10.21136/CMJ.2020.0451-19

Cité par Sources :