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Equations $ au\sp l\sb n=bu\sp k\sb m$ satisfied by members of recurrence sequences

Authors: H. P. Schlickewei and W. M. Schmidt
Journal: Proc. Amer. Math. Soc. 118 (1993), 1043-1051
MSC: Primary 11B37
MathSciNet review: 1152290
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Abstract: Let $ {\{ {u_n}\} _{n \in \mathbb{Z}}}$ be a linear recurrence sequence. Given $ a \ne 0,\,b \ne 0$, and natural $ k \ne l$, we study equations as indicated in the title in unknowns $ n,m$. It turns out that under natural conditions on the sequence $ \{ {u_n}\} $, there are only finitely many solutions.

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