Perfect squares representing the number of rational points on elliptic curves over finite field extensions

DOI10.1016/j.ffa.2020.101725zbMath1455.11053arXiv2003.09951OpenAlexW3046495637MaRDI QIDQ1994936

Kwok Chi Chim, Florian Luca

Publication date: 18 February 2021

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.09951

zbMATH Keywords

elliptic curvessubspace theoremrecurrence sequence

Mathematics Subject Classification ID

Rational points (14G05) Recurrences (11B37) Counting solutions of Diophantine equations (11D45) Elliptic curves (14H52) Diophantine inequalities (11J25) Exponential Diophantine equations (11D61) Schmidt Subspace Theorem and applications (11J87)

Related Items (1)

\(X\)-coordinates of Pell equations in various sequences

Cites Work

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• The zero multiplicity of linear recurrence sequences
• The equations \(2^N\pm 2^M\pm 2^L=z^2\)
• The Arithmetic of Elliptic Curves
• Perfect powers in linear recurring sequences
• A quantitative version of the Absolute Subspace Theorem
• The diophantine equation x²=p^a±p^b+1
• Zeros of recurrence sequences
• Abelian varieties over finite fields

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