On coprime integral solutions of \(y^ 2=x^ 3+k\)

DOI10.3792/pjaa.63.13zbMath0614.10017OpenAlexW2005498113MaRDI QIDQ1820194

Shoichi Kihara

Publication date: 1987

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.63.13

zbMATH Keywords

elliptic curvecubic diophantine equationconsecutive solutionsnumber of coprime integral solutions

Mathematics Subject Classification ID

Cubic and quartic Diophantine equations (11D25)

Related Items (3)

On the rank of the elliptic curve \(y^ 2=x^ 3+k\) ⋮ On the rank of the elliptic curve \(y^ 2=x^ 3+k\). II ⋮ Integral solutions in arithmetic progression for \(y^2 = x^3 + k\)

Cites Work

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• On the number of coprime integral solutions of \(y^ 2= x^ 3+k\)
• On the Diophantine Equation x³ +y³ +z³ = 1
• On Consecutive Integer Solutions for y 2 - k = x 3
• On the Number of Coprime Solutions of y 2 = x 3 + k
• Shorter Notes: A Note on Mordell's Equation y 2 = x 3 + k

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