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Products of prime powers in binary recurrence sequences. II. The elliptic case, with an application to a mixed quadratic-exponential equation

Author: B. M. M. de Weger
Journal: Math. Comp. 47 (1986), 729-739
MSC: Primary 11D61; Secondary 11Y50
MathSciNet review: 856716
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Abstract: In Part I the diophantine equation $ {G_n} = wp_1^{{m_1}} \cdots p_t^{{m_t}}$ was studied, where $ \{ {G_n}\} _{n = 0}^\infty $ is a linear binary recurrence sequence with positive discriminant. In this second part we extend this to negative discriminants. We use the p-adic and complex Gelfond-Baker theory to find explicit upper bounds for the solutions of the equation. We give algorithms to reduce those bounds, based on diophantine approximation techniques. Thus we have a method to solve the equation completely for arbitrary values of the parameters. We give an application to a quadratic-exponential equation.

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Article copyright: © Copyright 1986 American Mathematical Society

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