On Fibonacci numbers of the form \(q^ky^k\).

DOI10.1016/j.crma.2004.06.007zbMath1113.11010OpenAlexW2052526094MaRDI QIDQ1886964

Samir Siksek, Yann Bugeaud, Maurice Mignotte

Publication date: 23 November 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2004.06.007

zbMATH Keywords

Ribenboim's question

Mathematics Subject Classification ID

Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (10)

Terms of generalized Fibonacci sequences that are powers of their orders ⋮ Fibonacci and Lucas numbers of the form \(2^a+3^b+5^c\) ⋮ Products of Fibonacci numbers with indices in an interval and at most four omitted being a power ⋮ Generalized Fibonacci numbers of the form \(2^a + 3^b + 5^c\) ⋮ PERFECT POWERS THAT ARE SUMS OF TWO POWERS OF FIBONACCI NUMBERS ⋮ Fibonacci numbers at most one away from a perfect power ⋮ On \(px^{2}+q^{2n}=y^{p}\) and related Diophantine equations ⋮ On two-generator Fibonacci numerical semigroups with a prescribed genus ⋮ Almost powers in the Lucas sequence ⋮ On a class of Lebesgue-Ljunggren-Nagell type equations

Uses Software

• Magma
• PARI/GP

Cites Work

• The Magma algebra system. I: The user language
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• The terms Cx^h(h≥3) in Lucas sequences: an algorithm and applications to diophantine equations
• Sur les équations x^p+2^βy^p= z²et x^p+2^βy^p= 2z²
• Lucas and fibonacci numbers and some diophantine Equations

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