# Linear Equations over Multiplicative Groups, Recurrences, and Mixing II

Derksen, Harm and Masser, David. (2014) Linear Equations over Multiplicative Groups, Recurrences, and Mixing II. Preprints Fachbereich Mathematik, 2014 (17).

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Official URL: https://edoc.unibas.ch/70022/

Let $u_1,...,u_m$ be linear recurrences with values in a field K of positive characteristic p. We show that the set of integer vectors $(k_1,..., k_m)$ such that $u_1(k_1) +...+ u_m(k_m) = 0$ is p-normal in a natural sense generalizing that of the first author, who proved the result for m = 1. Furthermore the set is effectively computable if K is. We illustrate this with an example for m = 4. We also show that the corresponding set for zero charac- teristic is not decidable for m = 557844, thus verifying a conjecture of Cerlienco, Mignotte, and Piras.