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

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856716-7

MathSciNet review:
856716

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Abstract: In Part I the diophantine equation was studied, where 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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B. M. M. de Weger,*Products of prime powers in binary recurrence sequences. II. The elliptic case, with an application to a mixed quadratic-exponential equation*, Math. Comp.**47**(1986), no. 176, 729–739. MR**856716**, https://doi.org/10.1090/S0025-5718-1986-0856716-7**[5]**R. J. Stroeker and R. Tijdeman,*Diophantine equations*, Computational methods in number theory, Part II, Math. Centre Tracts, vol. 155, Math. Centrum, Amsterdam, 1982, pp. 321–369. MR**702521****[6]**Michel Waldschmidt,*A lower bound for linear forms in logarithms*, Acta Arith.**37**(1980), 257–283. MR**598881**

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0856716-7

Article copyright:
© Copyright 1986
American Mathematical Society