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August 2021 On solving a binary quadratic Diophantine equation
Keith R. Matthews, John P. Robertson
Rocky Mountain J. Math. 51(4): 1369-1385 (August 2021). DOI: 10.1216/rmj.2021.51.1369

Abstract

We look at methods for solving the Diophantine equation ax2+bxy+cy2+dx+ey+f=0 for which Δ=b24ac>0 and Δ is not a square. The methods we use transform this equation to one of the form AX2+BXY+CY2=N. We give upper limits on the number of solutions to the latter equation that need to be reviewed to determine all solutions to the original equation. These upper limits are substantially smaller than those generally given in the literature. We also discuss ways to compactly represent all solutions to the original equation.

Citation

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Keith R. Matthews. John P. Robertson. "On solving a binary quadratic Diophantine equation." Rocky Mountain J. Math. 51 (4) 1369 - 1385, August 2021. https://doi.org/10.1216/rmj.2021.51.1369

Information

Received: 23 November 2020; Accepted: 22 December 2020; Published: August 2021
First available in Project Euclid: 5 August 2021

Digital Object Identifier: 10.1216/rmj.2021.51.1369

Subjects:
Primary: 11D09, 11D85

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 4 • August 2021
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