An algorithm to determine the points with integral coordinates in certain elliptic curves

DOI10.1006/jnth.1998.2290zbMath0923.11036OpenAlexW2002126705MaRDI QIDQ1284196

Paulo Ribenboim

Publication date: 18 October 1999

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

Full work available at URL: https://doi.org/10.1006/jnth.1998.2290

zbMATH Keywords

elliptic curveLucas sequence

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (4)

On some Diophantine equations ⋮ Perfect powers from products of terms in Lucas sequences ⋮ Integral points on the elliptic curve \(E_{ pq }\): \(y^2 = x^3 + ( pq - 12) x - 2( pq - 8)\) ⋮ Unnamed Item

Cites Work

• Perfect powers in second order linear recurrences
• On squares in certain Lucas sequences
• The square terms in Lucas sequences
• Some quartic Diophantine equations
• Squares in some recurrent sequences
• On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.
• The Fibonacci numbers and the Arctic Ocean
• Lucas and fibonacci numbers and some diophantine Equations
• On Square Fibonacci Numbers
• Eight Diophantine Equations
• Some Remarks on the Diophantine Equations x ² − Dy ⁴ = 1 and x ⁴ − Dy ² = 1
• The Diophantine Equation y ² = Dx ⁴ +1
• Five Diophantine Equations.
• The Diophantine Equation $3x^4-2y^2=1$.
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