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Multiplicities of second order linear recurrences. (English) Zbl 0269.10005


MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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[1] R. Alter and K. K. Kubota, The diophantine equation \( {x^2} + 11 = {3^n}\), and a related sequence, J. Number Theory (to appear). · Zbl 0293.10010
[2] Roger Apéry, Sur une équation diophantienne, C. R. Acad. Sci. Paris 251 (1960), 1263 – 1264 (French). · Zbl 0093.04703
[3] P. Chowla, S. Chowla, M. Dunton, and D. J. Lewis, Some diophantine equations in quadratic number fields, Norske Vid. Selsk. Forh. 31 (1958), 181 – 183. · Zbl 0088.03703
[4] S. Chowla, M. Dunton, and D. J. Lewis, Linear recurrences of order two, Pacific J. Math. 11 (1961), 833 – 845. · Zbl 0106.03501
[5] R. R. Laxton, Linear recurrences of order two, J. Austral. Math. Soc. 7 (1967), 108 – 114. · Zbl 0146.05005
[6] D. J. Lewis, Diophantine equations: \?-adic methods, Studies in Number Theory, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1969, pp. 25 – 75.
[7] Andrzej Schinzel, The intrinsic divisors of Lehmer numbers in the case of negative discriminant, Ark. Mat. 4 (1962), 413 – 416 (1962). · Zbl 0106.03105 · doi:10.1007/BF02591623
[8] Thoralf Skolem, S. Chowla, and D. J. Lewis, The diophantine equation 2\(^{n}\)\(^{+}\)²-7=\?² and related problems, Proc. Amer. Math. Soc. 10 (1959), 663 – 669. · Zbl 0089.26701
[9] Morgan Ward, The null divisors of linear recurring series, Duke Math. J. 2 (1936), no. 3, 472 – 476. · Zbl 0015.15506 · doi:10.1215/S0012-7094-36-00240-5
[10] -, Some diophantine problems connected with linear recurrences, Report of the Institute of the Theory of Numbers, University of Colorado, Boulder, 1959, pp. 250-257.
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