Skolem's exponential local-global principle for simple rational LRBS

Let $\boldsymbol u=\langle u_n\rangle_{n=-\infty}^{\infty}$ be a simple rational LRBS taking values in $\mathbb{Z}[\frac{1}{b}]$ for some non-zero integer $b$. A sequence has no zero when $u_n\neq 0$ for every $n\in\mathbb{Z}$. Skolem's exponential local-global principle. The sequence $\boldsymbol u$ has no zero if and only if there is an integer $m\geq 2$ with $\gcd(b,m)=1$ such that $u_n\not\equiv 0\pmod m$ for every $n\in\mathbb{Z}$. This principle says that the absence of an integer zero in a simple rational LRBS should be witnessed by a single modulus; it is introduced as a conjecture motivating the Bi-Skolem Problem, and its status is not resolved in the supplied source.