Integer points on the elliptic curve with Fibonacci numbers

DOI10.1007/S13226-023-00378-2MaRDI QIDQ6572369

Jinseo Park

Publication date: 15 July 2024

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

elliptic curveFibonacci numbersDiophantine \(m\)-tuple

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Elliptic curves over global fields (11G05) Counting solutions of Diophantine equations (11D45) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

• The Hoggatt-Bergum conjecture on \(D(-1)\)-triples \(\{F_{2k+1}\), \(F_{2k+3}\), \(F_{2k+5}\}\) and integer points on the attached elliptic curves
• Diophantine \(m\)-tuples and elliptic curves
• Some family of Diophantine pairs with Fibonacci numbers
• Diophantine triples of Fibonacci numbers
• The extendibility of diophantine pairs I: the general case
• A proof of the Hoggatt-Bergum conjecture
• A parametric family of elliptic curves
• On Diophantine quadruples of Fibonacci numbers
• There is no Diophantine quintuple
• Euler's concordant forms
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
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