On \(k\)-generalized Fibonacci Diophantine triples

MaRDI QIDQ6621967

N. Irmak

Publication date: 21 October 2024

Published in: Mathematical Communications (Search for Journal in Brave)

zbMATH Keywords

Diophantine triples\(k\)-generalized Fibonacci number

Mathematics Subject Classification ID

Diophantine equations in many variables (11D72) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Cites Work

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• Diophantine triples and \(k\)-generalized Fibonacci sequences
• An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. II
• Powers of two in generalized Fibonacci sequences
• On a conjecture about repdigits in \(k\)-generalized Fibonacci sequences
• Lucas Diophantine Triples
• Fibonacci Diophantine triples
• Diophantine quadruples with values in k-generalized Fibonacci numbers
• Only finitely many Tribonacci Diophantine triples exist
• Powers of two as sums of two k-Fibonacci numbers
• A simplified Binet formula for k-generalized Fibonacci numbers
• Diophantine triples and reduced quadruples with the Lucas sequence of recurrence un=Aun-1-un-2
• The complete solution of the Diophantine equation \(\left(F_{n+1}^{(k)}\right)^x - \left(F_{n-1}^{(k)}\right)^x = F_m^{(k)}\)

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