The nonlinear Skolem–Mahler–Lech conjecture

Let $l\geq 1$, let $F\in\mathbb{C}[x_0,\dots,x_{l-1}]$, and let $\{A_n\}_{n\geq 0}$ be a recurrence sequence satisfying

$$A_{n+l}=F(A_n,\dots,A_{n+l-1})$$

for all $n\geq 0$. The nonlinear Skolem–Mahler–Lech conjecture. The zero set

$$\{n\geq 0\mid A_n=0\}$$

is a union of at most finitely many arithmetic progressions. This is a nonlinear analogue of the classical Skolem–Mahler–Lech theorem and is implied by the dynamical Mordell–Lang conjecture for a corresponding polynomial map; the paper notes it is known for $l=2$ in the cited cases.