Fibonacci and Lucas numbers of the form \(2^a+3^b+5^c\)

DOI10.3792/pjaa.89.47zbMath1362.11018OpenAlexW2089440894MaRDI QIDQ376538

Diego Marques, Alain S. Togbé

Publication date: 5 November 2013

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pja/1362146478

zbMATH Keywords

Fibonaccilinear forms in logarithmsreduction methodLucas

Mathematics Subject Classification ID

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

Related Items (9)

Terms of generalized Fibonacci sequences that are powers of their orders ⋮ On the exponential Diophantine equation \(F_n^x+F_{n+1}^x+\cdots+F_{n+k-1}^x=F_m\) ⋮ \(k\)-Fibonacci powers as sums of powers of some fixed primes ⋮ Linear combinations of prime powers in binary recurrence sequences ⋮ Unnamed Item ⋮ Pell and Pell-Lucas numbers of the form \(x^a\pm x^b+1\) ⋮ Generalized Fibonacci numbers of the form \(2^a + 3^b + 5^c\) ⋮ Linear combinations of prime powers in sums of terms of binary recurrence sequences ⋮ Linear combinations of prime powers in \(X\)-coordinates of Pell equations

Cites Work

• Fibonacci numbers at most one away from a perfect power
• On Fibonacci numbers of the form \(q^ky^k\).
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• Linear forms in two logarithms and interpolation determinants II
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