Geodesic
On fundamental solutions of binary quadratic form equations
Keith R. Matthews1 ; John P. Robertson2 ; Anitha Srinivasan3
1 Department of Mathematics University of Queensland Brisbane 4072, Australia and Centre for Mathematics and its Applications Australian National University Canberra, ACT 0200, Australia
2 Actuarial and Economic Services Division National Council on Compensation Insurance Boca Raton, FL 33487, U.S.A.
3 Department of Mathematics Saint Louis University – Madrid campus Avenida del Valle 34 28003 Madrid, Spain
Acta Arithmetica, Tome 169 (2015) no. 3, pp. 291-299.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation $Au^2+Buv+Cv^2=N$, where $A>0$, $N\not =0$ and $B^2-4AC$ is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation $u^2-dv^2=N$, where $d$ is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.
DOI : 10.4064/aa169-3-4
Keywords: suitable modification upper bound estimates stolt fundamental integer solutions diophantine equation buv where positive nonsquare characterize fundamental solutions corollary get corresponding result equation dv where positive nonsquare which upper bound estimates obtained nagell chebyshev

Keith R. Matthews 1 ; John P. Robertson 2 ; Anitha Srinivasan 3

1 Department of Mathematics University of Queensland Brisbane 4072, Australia and Centre for Mathematics and its Applications Australian National University Canberra, ACT 0200, Australia
2 Actuarial and Economic Services Division National Council on Compensation Insurance Boca Raton, FL 33487, U.S.A.
3 Department of Mathematics Saint Louis University – Madrid campus Avenida del Valle 34 28003 Madrid, Spain 
@article{10_4064_aa169_3_4,
     author = {Keith R. Matthews and John P. Robertson and Anitha Srinivasan},
     title = {On fundamental solutions of binary quadratic form equations},
     journal = {Acta Arithmetica},
     pages = {291--299},
     publisher = {mathdoc},
     volume = {169},
     number = {3},
     year = {2015},
     doi = {10.4064/aa169-3-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa169-3-4/}
}
TY  - JOUR
AU  - Keith R. Matthews
AU  - John P. Robertson
AU  - Anitha Srinivasan
TI  - On fundamental solutions of binary quadratic form equations
JO  - Acta Arithmetica
PY  - 2015
SP  - 291
EP  - 299
VL  - 169
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa169-3-4/
DO  - 10.4064/aa169-3-4
LA  - en
ID  - 10_4064_aa169_3_4
ER  - 
%0 Journal Article
%A Keith R. Matthews
%A John P. Robertson
%A Anitha Srinivasan
%T On fundamental solutions of binary quadratic form equations
%J Acta Arithmetica
%D 2015
%P 291-299
%V 169
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa169-3-4/
%R 10.4064/aa169-3-4
%G en
%F 10_4064_aa169_3_4
Keith R. Matthews; John P. Robertson; Anitha Srinivasan. On fundamental solutions of binary quadratic form equations. Acta Arithmetica, Tome 169 (2015) no. 3, pp. 291-299. doi : 10.4064/aa169-3-4. http://geodesic.mathdoc.fr/articles/10.4064/aa169-3-4/

Cité par Sources :