Let $\mathbb{N}$ be the set of positive integers and $\lambda:\mathbb{N}\to \{-1,1\}$ the Liouville function. This function is defined as follows: if $n=1$, we define $\lambda(1)=1$; if $n\geq 2$ and its decomposition in prime factors is given by $n=p_1^{r_1}\ldots p_k^{r_k}$, we define $\lambda(n)=(-1)^{r_1+\ldots+r_k}$.
The Liouville sequence is $(\lambda(1),\lambda(2),\ldots)\in \{-1,1\}^{\mathbb{N}}$. Given $n\geq 1$ and a (finite) fixed string $(x_1,\ldots,x_n)\in\{-1,1\}^{n}$, how can we prove that such string appears somewhere in the Liouville sequence? More precisely, how can we prove that there is some integer $k\geq 0$ such that $(x_1,\ldots,x_n)=(\lambda(k+1),\lambda(k+2),\ldots,\lambda(k+n))$?