On the exponential Diophantine equation Pxn+Pxn+1=Pm

DOI10.3906/mat-1810-130zbMath1455.11056OpenAlexW2947597265WikidataQ115483985 ScholiaQ115483985MaRDI QIDQ5229867

Florian Luca, Bernadette Faye, Salah Eddine Rihane, Alain S. Togbé

Publication date: 19 August 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-1810-130

zbMATH Keywords

reduction methodPell numberslinear form in logarithms

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Related Items (12)

An exponential Diophantine equation involving the sum or difference of powers of two Pell numbers ⋮ On the exponential Diophantine equation \(F_{n+1}^x - F_{n-1}^x = F_m^y\) ⋮ The Diophantine equations \(P_n^x+P_{n+1}^y=P_m^x\) or \(P_n^y+P_{n+1}^x=P_m^x\) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ An exponential Diophantine equation related to powers of three consecutive Fibonacci numbers ⋮ On the exponential Diophantine equation P^x _n + P ^x _n+1 + ⋯ + P ^x _n+k-1 = P_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 ⋮ On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences ⋮ Pell-Lucas numbers as sum of same power of consecutive Pell numbers ⋮ On the Diophantine equation \(P_m=P_n^x+P_{n+1}^x\) with Padovan numbers ⋮ On the exponential Diophantine equation Fnx ± Fmx = a with a ∈{Fr,Lr}

Cites Work

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• On the sum of powers of two consecutive Fibonacci numbers
• Coincidences in generalized Fibonacci sequences
• 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
• An exponential Diophantine equation related to the sum of powers of two consecutive k-generalized Fibonacci numbers
• Linear combinations of prime powers in binary recurrence sequences
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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