Diophantine equations with products of consecutive members of binary recurrences. (English) Zbl 1431.11045
Summary: We prove a finiteness result for the number of solutions of a Diophantine equation of the form
\[u_n u_{n+1}\cdots u_{n+k}\pm 1 =\pm u_m^2, \]
where \(\{ u_n\}_{n\geq 1}\) is a binary recurrent sequence whose characteristic equation has roots which are real quadratic units.
\[u_n u_{n+1}\cdots u_{n+k}\pm 1 =\pm u_m^2, \]
where \(\{ u_n\}_{n\geq 1}\) is a binary recurrent sequence whose characteristic equation has roots which are real quadratic units.
MSC:
| 11D61 | Exponential Diophantine equations |
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
| 11J86 | Linear forms in logarithms; Baker’s method |
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