On fundamental solutions of binary quadratic form equations

Keith R. Matthews, John P. Robertson, and Anitha Srinivasan. "On fundamental solutions of binary quadratic form equations." Acta Arithmetica 169.3 (2015): 291-299. <http://eudml.org/doc/278934>.

@article{KeithR2015,
abstract = {We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation Au²+Buv+Cv²=N, where A>0, N≠0 and B²-4AC is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation u²-dv²=N, where d is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.},
author = {Keith R. Matthews, John P. Robertson, Anitha Srinivasan},
journal = {Acta Arithmetica},
keywords = {Diophantine equation; indefinite binary quadratic form; equivalence class; fundamental solution},
language = {eng},
number = {3},
pages = {291-299},
title = {On fundamental solutions of binary quadratic form equations},
url = {http://eudml.org/doc/278934},
volume = {169},
year = {2015},
}

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
VL - 169
IS - 3
SP - 291
EP - 299
AB - We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation Au²+Buv+Cv²=N, where A>0, N≠0 and B²-4AC is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation u²-dv²=N, where d is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.
LA - eng
KW - Diophantine equation; indefinite binary quadratic form; equivalence class; fundamental solution
UR - http://eudml.org/doc/278934
ER -