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

DOI10.1216/RMJ-2009-39-6-1907zbMath1248.11025WikidataQ123328432 ScholiaQ123328432MaRDI QIDQ1047546

Yasutsugu Fujita

Publication date: 5 January 2010

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Elliptic curves over global fields (11G05) Cubic and quartic Diophantine equations (11D25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (10)

Diophantine triple with Fibonacci numbers and elliptic curve ⋮ On the \(D(- 1)\)-triple \(\{ 1,k^{2}+1,k^{2}+2k+2\}\) and its unique \(D(1)\)-extension ⋮ Unnamed Item ⋮ Compact representation of quadratic integers and integer points on some elliptic curves ⋮ There is no Diophantine D(−1)$D(-1)$‐quadruple ⋮ Some family of Diophantine pairs with Fibonacci numbers ⋮ Unnamed Item ⋮ The extendibility of Diophantine pairs with property $D(-1)$ ⋮ On the family of Diophantine triples \(\{k+1,4k,9k+3\}\) ⋮ On a family of Diophantine triples \(\{k,A^2k+2A,(A+1)^2k+2(A+1)\}\) with two parameters

Uses Software

• ecdata

Cites Work

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