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Mathematics of Computation

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Arithmetical study of a certain ternary recurrence sequence and related questions

Authors: M. Mignotte and N. Tzanakis
Journal: Math. Comp. 61 (1993), 901-913
MSC: Primary 11B37
MathSciNet review: 1185248
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Abstract: The complete solution in $ (n,{y_1},{y_2}) \in {{\mathbf{Z}}^3}$ of the Diophantine equation

$\displaystyle {b_n} = \pm {2^{{y_1}}}{3^{{y_2}}}$

is given, where $ {({b_n})_{n \in {\mathbf{Z}}}}$ is Berstel's recurrence sequence defined by

$\displaystyle {b_0} = {b_1} = 0,\quad {b_2} = 1,\quad {b_{n + 3}} = 2{b_{n + 2}} - 4{b_{n + 1}} + 4{b_n}.$

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Article copyright: © Copyright 1993 American Mathematical Society

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