Products of prime powers in binary recurrence sequences. II. The elliptic case, with an application to a mixed quadratic-exponential equation
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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- P. Kiss, "Zero terms in second order linear recurrences," Math. Sem. Notes Kobe Univ., v. 7, 1979, pp. 145-152. MR 544926 (80j:10015)
- K. Mahler, "Eine arithmetische Eigenschaft der rekurrierenden Reihen," Mathematika B (Leiden), v. 3, 1934, pp. 153-156.
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- M. Waldschmidt, "A lower bound for linear forms in logarithms," Acta Arith., v. 37, 1980, pp. 257-283. MR 598881 (82h:10049)