Let $a\_1=0$, $a\_2=\alpha$, and $a\_n=\lambda a\_{n-1}+\mu a\_{n-2}$ for $n\geq 3$. 

Are there positive integers $\alpha$, $\lambda$, $\mu$ such that 
$$a\_{p^2} \equiv 0 \mod p $$
for every prime $p>2$?