Question 81
Given a pair $(a_{0}, b_{0})$ of real numbers, we define two sequences $a_{0}, a_{1}, a_{2}, \ldots$ and $b_{0}, b_{1}, b_{2}, \ldots$ of real numbers by
$$
a_{n+1}=a_{n}+b_{n} \quad \text{ and } \quad b_{n+1}=a_{n} \cdot b_{n}
$$
for all $n=0,1,2, \ldots$ Find all pairs $(a_{0}, b_{0})$ of real numbers such that $a_{2022}=a_{0}$ and $b_{2022}=b_{0}$.
$$
a_{n+1}=a_{n}+b_{n} \quad \text{ and } \quad b_{n+1}=a_{n} \cdot b_{n}
$$
for all $n=0,1,2, \ldots$ Find all pairs $(a_{0}, b_{0})$ of real numbers such that $a_{2022}=a_{0}$ and $b_{2022}=b_{0}$.