2 problems

Rampersad–Shallit conjecture. The sequence of Motzkin numbers modulo $p$ is uniformly recurrent if and only if $T_n\bmod p$ is never $0$.

Let $P$ be a univariate Laurent polynomial and let $p$ be prime. For the constant term sequence $A_p(n)=\operatorname{ct}[P^n]\bmod p$, suppose there exists some $n\in\mathbb{N}$ s…