On the sum of squares of consecutive $k$-bonacci numbers which are $l$-bonacci numbers

DOI10.4064/cm7272-6-2018zbMath1452.11021OpenAlexW2908697971MaRDI QIDQ5742277

Diego Marques, Gérsica Freitas, Pavel Trojovský, Dušan Bednařík

Publication date: 13 May 2019

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/cm7272-6-2018

zbMATH Keywords

linear forms in logarithmsreduction methodDiophantine equationsgeneralized Fibonacci sequences

Mathematics Subject Classification ID

Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86) Diophantine equations (11D99)

Related Items (5)

On the exponential Diophantine equation \(F_{n+1}^x - F_{n-1}^x = F_m^y\) ⋮ On Fibonacci numbers as sum of powers of two consecutive tribonacci numbers ⋮ An exponential Diophantine equation related to powers of three consecutive Fibonacci numbers ⋮ On the exponential Diophantine equation \(F_{n+1}^x - F_{n-1}^x = F_m\) ⋮ An exponential Diophantine equation related to the sum of powers of two consecutive terms of a Lucas sequence and \(x\)-coordinates of Pell equations

Cites Work

• On the sum of powers of two consecutive Fibonacci numbers
• An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• ON THE LARGEST PRIME FACTOR OF THE k-FIBONACCI NUMBERS
• On a conjecture about repdigits in k-generalized Fibonacci sequences
• The Fibonacci Numbers: Exposed
• A simplified Binet formula for k-generalized Fibonacci numbers
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