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December 2020 On the equation $y^2=x^6+k$
Xuan Tho Nguyen
Rocky Mountain J. Math. 50(6): 2167-2178 (December 2020). DOI: 10.1216/rmj.2020.50.2167

Abstract

We find all rational solutions to the equation y2=x6+k, where k=39 or k=47. These are the two unsolved cases for k in the range |k|50. Our method is elementary and can be applied to other situations to find all rational points on certain curves of genus 2.

Citation

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Xuan Tho Nguyen. "On the equation $y^2=x^6+k$." Rocky Mountain J. Math. 50 (6) 2167 - 2178, December 2020. https://doi.org/10.1216/rmj.2020.50.2167

Information

Received: 10 June 2020; Revised: 3 July 2020; Accepted: 3 July 2020; Published: December 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/rmj.2020.50.2167

Subjects:
Primary: 14G05, 14G25
Secondary: 11R04

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 6 • December 2020
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