Abstract
Let Gn be a second order linear recursive sequence, which satisfy certain conditions, and p be a prime. In this paper we describe an algorithm with which one can compute all but possible one integer solutions n,z of the diophantine equation Gn=pz. In the exceptional case the algorithm gives an n such that Gn is the only possible further power of p. We give an upper bound for the running time too.
This work was written when the author was a visitor at the Universität zu Köln with the fellowship of the Alexander von Humboldt-Stiftung.
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References
F. Beukers, The generalized Ramanujan-Nagell equation, Ph.D. Thesis, University of Leiden, 1979.
E.L. Cohen, The diophantine equation x2+11=3k and related questions, Math. Scand., 38 (1976), 240–246.
P. Kiss and B.M. Phong, Divisibility properties in second order recurrences, Publ. Math. Debrecen, 26 (1979), 187–197.
E. Lucas, Sur la théorie des nombres premiers, Atti R. Accad.Sc. Torino (math.) 11 (1875–76), 928–937.
E. Lucas, Théorie des fonctions numériques simplements périodiques, Amer. J. Math., 1 (1878), 184–240, 289–321.
M. Mignotte, On the automatic resolution of certain diophantine equations, EUROSAM 84, Lect. Notes in Computer Sc. 174, 378–385, Springer Verlag 1984.
A. Schinzel, On two theorems of Gelfond and some of their applications, Acta Arith. 13 (1967), 177–236.
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© 1985 Springer-Verlag Berlin Heidelberg
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Pethö, A. (1985). On the solution of the diophantine equation Gn=pz . In: Caviness, B.F. (eds) EUROCAL '85. EUROCAL 1985. Lecture Notes in Computer Science, vol 204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15984-3_320
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DOI: https://doi.org/10.1007/3-540-15984-3_320
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