Question 178
Let $\left(a_{n}\right)_{n \geq 0}$ and $\left(b_{n}\right)_{n \geq 0}$ be sequences defined by $a_{n+2}= a_{n+1}+a_{n}$, $n=0,1, \ldots$, $a_{0}=1$, $a_{1}=2$, and $b_{n+2}=b_{n+1}+b_{n}$, $n=0,1, \ldots$, $b_{0}=2$, $b_{1}=1$. How many integers do the sequences have in common?