Abstract
We give an algorithm for the computation of Pell numbers of the form \(P_n=px^2,\) where p is prime and \(x \in {ZZ}\).
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Bugeaud, Y.: On the size of integer solutions of elliptic equations. Bull. Austral. Math. Soc. 57(2), 199–206 (1998)
Cohen, H.: Advanced topics in computational number theory. Graduate Texts in Mathematics, vol. 193., pp. xvi+578. Springer, New York (2000)
Egge, E.S., Mansour, T.: 132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers. Discrete Appl. Math. 143(1-3), 72–83 (2004)
Hardy, K., Hudson, R.H., Richman, D., Williams, K.S.: Determination of all imaginary cyclic quartic fields with class number 2. Trans. Am. Math. Soc. 311(1), 1–55 (1989)
Huard, J.G., Spearman, B.K., Williams, K.S.: Integral bases for quartic fields with quadratic subfields. J. Number Theory 51(1), 87–102 (1995)
Kappe, L.-C., Warren, B.: An elementary test for the Galois group of a quartic polynomial. Amer. Math. Monthly 96(2), 133–137 (1989)
Ljunggren, W.: Zur Theorie der Gleichung x2 + 1 = Dy4. Avh. Norsk. Vid. Akad. Oslo, 1–27 (1942)
McDaniel, W.L.: On Fibonacci and Pell numbers of the form kx2 (Almost every term has a 4r + 1 prime factor). Fibonacci Q. 40(1), 41–42 (2002)
Pethö, A.: Full cubes in the Fibonacci sequence. Publ. Math. Debrecen 30, 117–127 (1983)
Poulakis, D.: Integer points on algebraic curves with exceptional units. J. Austral. Math. Soc. Ser. A 63(2), 145–164 (1997)
Ribenboim, P.: Pell numbers, squares and cubes. Publ. Math. Debrecen 54(1-2), 131–152 (1999)
Robbins, N.: On Pell numbers of the form \(px\sp 2\), where p is prime. Fibonacci Quart 22(4), 340–348 (1984)
Silverman, J.H.: The Aritmetic of Elliptic Curves. Springer, Heidelberg (1986)
Sloane, N.J.A.: An On-Line Version of the Encyclopedia of Integer Sequences, http://www.research.att.com/~njas/sequences/A000129
Wildanger, K.: Über das Lösen von Einheiten- und Indexformgleichungen in algebraischen Zahlkörpern (German) [Solving unit and index form equations in algebraic number fields]. J. Number Theory 82(2), 188–224 (2000)
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Draziotis, K.A. (2009). Computation of Pell Numbers of the Form pX 2 . In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2009. Lecture Notes in Computer Science, vol 5725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03564-7_14
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DOI: https://doi.org/10.1007/978-3-642-03564-7_14
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