Geodesic
On the Skolem problem and some related questions for parametric families of linear recurrence sequences
Canadian journal of mathematics, Tome 74 (2022) no. 3, pp. 773-792

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DOI

We show that in a parametric family of linear recurrence sequences $a_1(\alpha ) f_1(\alpha )^n + \cdots + a_k(\alpha ) f_k(\alpha )^n$ with the coefficients $a_i$ and characteristic roots $f_i$, $i=1, \ldots ,k$, given by rational functions over some number field, for all but a set of elements $\alpha $ of bounded height in the algebraic closure of ${\mathbb Q}$, the Skolem problem is solvable, and the existence of a zero in such a sequence can be effectively decided. We also discuss several related questions.
DOI : 10.4153/S0008414X21000080
Mots-clés : Skolem problem, perfect power, linear recurrence sequence 
Ostafe, Alina; Shparlinski, Igor E. On the Skolem problem and some related questions for parametric families of linear recurrence sequences. Canadian journal of mathematics, Tome 74 (2022) no. 3, pp. 773-792. doi: 10.4153/S0008414X21000080
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     title = {On the {Skolem} problem and some related questions for parametric families of linear recurrence sequences},
     journal = {Canadian journal of mathematics},
     pages = {773--792},
     year = {2022},
     volume = {74},
     number = {3},
     doi = {10.4153/S0008414X21000080},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000080/}
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