The Diophantine equations \(P_n^x+P_{n+1}^y=P_m^x\) or \(P_n^y+P_{n+1}^x=P_m^x\)
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Publication:6042183
DOI10.1007/s13398-023-01425-7zbMath1517.11010MaRDI QIDQ6042183
Alain S. Togbé, Bernadette Faye, Florian Luca, Salah Eddine Rihane
Publication date: 16 May 2023
Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)
Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86) Diophantine equations (11D99)
Cites Work
- On the Diophantine equation \(F_n^x+F_{n+1}^x=F_m^y\)
- On the sum of powers of two consecutive Fibonacci numbers
- Effective lower bound for the \(p\)-adic distance between powers of algebraic numbers
- Linear forms in two logarithms and interpolation determinants
- Linear combinations of factorials and \(S\)-units in a binary recurrence sequence
- An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers
- Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
- An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
- Primary cyclotomic units and a proof of Catalans conjecture
- On the exponential Diophantine equation Pxn+Pxn+1=Pm
- Number Theory
- Unnamed Item
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