On fundamental solutions of binary quadratic form equations

• Autorzy: Keith R. Matthews , John P. Robertson , Anitha Srinivasan
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11A55: Continued fractions
• 11D45: Counting solutions of Diophantine equations
• 11D09: Quadratic and bilinear equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 169
• Numer: 3
• Strony: 291-299

Daty

wydano

2015

Twórcy

autor

Keith R. Matthews

• Department of Mathematics, University of Queensland, Brisbane 4072, Australia
• Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia

autor

John P. Robertson

• Actuarial and Economic Services Division, National Council on Compensation Insurance, Boca Raton, FL 33487, U.S.A.

autor

Anitha Srinivasan

• Department of Mathematics, Saint Louis University - Madrid campus, Avenida del Valle 34, 28003 Madrid, Spain

Identyfikatory

DOI

10.4064/aa169-3-4