I2.3 Let $f(1)=3, f(2)=5$ and $f(n+2)=f(n+1)+f(n)$ for positive integers $n$. If $c$ is the remainder of $f(b)$ divided by 3 , find the value of $c$.
$$
\begin{aligned}
f(1)=3, f(2)=5, f(3)=8, f(4)=13, f(5)=21, f(6)=34, f(7)=55, f(8)=89, \\
\equiv 0, \quad \equiv 2, \quad \equiv 2, \quad \equiv 1, \quad \equiv 0, \quad \equiv 1, \quad \equiv 1, \quad \equiv 2(\bmod 3)
\end{aligned}
$$
$$
f(9) \equiv 0, f(10) \equiv 2, f(11) \equiv 2, f(12) \equiv 1, f(13) \equiv 0, f(14) \equiv 1, f(15) \equiv 1, f(16) \equiv 2(\bmod 3)
$$
$\therefore$ When $f(n)$ is divided by 3 , the pattern of the remainders repeats for every 8 integers.
$$
\begin{array}{l}
600=8 \times 75 \\
c=2
\end{array}
$$