On a problem of Pillai with Fibonacci numbers and powers of 2

DOI10.1007/s12044-017-0338-3zbMath1421.11017arXiv1707.07229OpenAlexW2612283539MaRDI QIDQ2401131

Mahadi Ddamulira, Florian Luca, Mihaja Rakotomalala

Publication date: 31 August 2017

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.07229

zbMATH Keywords

Fibonacci numberslinear forms in logarithmsreduction method

Mathematics Subject Classification ID

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

Related Items (20)

On a variant of Pillai problem: integers as difference between generalized Pell numbers and perfect powers ⋮ On a variant of Pillai's problem involving \(S\)-units and Fibonacci numbers ⋮ On a variant of Pillai's problem. II. ⋮ Unnamed Item ⋮ Laplace-Fibonacci transform by the solution of second order generalized difference equation ⋮ On a problem of Pillai with Fibonacci numbers and powers of 3 ⋮ On a variant of Pillai’s problem with binary recurrences and S-units ⋮ On a variant of Pillai's problem with factorials and \(S\)-units ⋮ On the Diophantine equation 𝑈_{𝑛}-𝑏^{𝑚}=𝑐 ⋮ On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3 ⋮ On Pillai’s problem with X-coordinates of Pell equations and powers of 2 II ⋮ On Pillai's problem with the Fibonacci and Pell sequences ⋮ Integers representable as differences of linear recurrence sequences ⋮ On Diophantine equations involving sums of Fibonacci numbers and powers of $2$ ⋮ A Hasse-type principle for exponential Diophantine equations over number fields and its applications ⋮ On a problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of 2 ⋮ On a variant of Pillai’s problem ⋮ Pillai's problem with k-Fibonacci and Pell numbers ⋮ On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime ⋮ On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3

Cites Work

• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On a problem of Pillai with Fibonacci numbers and powers of 2