Products of prime powers in binary recurrence sequences. II. The elliptic case, with an application to a mixed quadraticexponential equation
Author:
B. M. M. de Weger
Journal:
Math. Comp. 47 (1986), 729739
MSC:
Primary 11D61; Secondary 11Y50
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 padic and complex GelfondBaker 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 quadraticexponential equation.
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 A. Baker & H. Davenport, "The equations and ," Quart. J. Math. Oxford Ser. (2), v. 20, 1969, pp. 129137. MR 0248079 (40:1333)
 [2]
 P. Kiss, "Zero terms in second order linear recurrences," Math. Sem. Notes Kobe Univ., v. 7, 1979, pp. 145152. MR 544926 (80j:10015)
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 K. Mahler, "Eine arithmetische Eigenschaft der rekurrierenden Reihen," Mathematika B (Leiden), v. 3, 1934, pp. 153156.
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 A. Pethö & B. M. M. de Weger, "Products of prime powers in binary recurrence sequences. I," Math. Comp., v. 47, 1986, pp. 713727. MR 856715 (87m:11027a)
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 R. J. Stroeker & R. Tijdeman, "Diophantine equations," in Computational Methods in Number Theory (H. W. Lenstra, Jr. and R. Tijdeman, eds.), MC Tract 155, Amsterdam, 1982, pp. 321369. MR 702521 (84i:10014)
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 M. Waldschmidt, "A lower bound for linear forms in logarithms," Acta Arith., v. 37, 1980, pp. 257283. MR 598881 (82h:10049)
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DOI:
http://dx.doi.org/10.1090/S00255718198608567167
PII:
S 00255718(1986)08567167
Article copyright:
© Copyright 1986
American Mathematical Society
