Arithmetical study of a certain ternary recurrence sequence and related questions

Mignotte, M.; Tzanakis, N.

doi:10.1090/S0025-5718-1993-1185248-8

Arithmetical study of a certain ternary recurrence sequence and related questions
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by M. Mignotte and N. Tzanakis PDF

Math. Comp. 61 (1993), 901-913 Request permission

Abstract:

The complete solution in $(n,{y_1},{y_2}) \in {{\mathbf {Z}}^3}$ of the Diophantine equation \[ {b_n} = \pm {2^{{y_1}}}{3^{{y_2}}}\] is given, where ${({b_n})_{n \in {\mathbf {Z}}}}$ is Berstel’s recurrence sequence defined by \[ {b_0} = {b_1} = 0,\quad {b_2} = 1,\quad {b_{n + 3}} = 2{b_{n + 2}} - 4{b_{n + 1}} + 4{b_n}.\]

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