The Legendre equation in Euclidean imaginary quadratic number fields

DOI10.1016/J.JNT.2017.10.012zbMath1444.11048OpenAlexW2770460066MaRDI QIDQ1711713

Gustavo Vargas de los Santos, Javier Diaz-Vargas

Publication date: 18 January 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2017.10.012

zbMATH Keywords

imaginary quadratic number fieldsEuclidean domainsLegendre equation

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Quadratic and bilinear Diophantine equations (11D09) General ternary and quaternary quadratic forms; forms of more than two variables (11E20)

Cites Work

• Unnamed Item
• On the magnitude of the Gaussian integer solutions of the Legendre equation
• On the magnitude of the integer solutions of the equation \(ax^ 2 +by^ 2 +cz^ 2 = 0\)
• On the solvability of the Diophantine equation \({ax^2+by^2+cz^2=0 }\) in imaginary Euclidean quadratic fields
• Minimal Solutions of Diophantine Equations
• An Equation in Gaussian Integers

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