On The diophantine equation Fn+Fm=2a |
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| Authors: | Jhon J Bravo |
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| Institution: | Departamento de Matemáticas, Universidad del Cauca, Calle 5 No 4–70, Popayán, Cauca, Colombia. E-Mail jbravo@unicauca.edu.co |
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| Abstract: | In this paper, we find all the solutions of the title Diophantine equation in positive integer variables (n, m, a), where Fk is the kth term of the Fibonacci sequence. The proof of our main theorem uses lower bounds for linear forms in logarithms (Baker's theory) and a version of the Baker-Davenport reduction method in diophantine approximation. |
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| Keywords: | 11B39 11J86 11D61 |
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