Question 44
In the Cartesian plane, an integer point is called an entire coordinate point. If $n$ is a positive integer, let $f(n)$ be the number of integer points that are on the segment that connects the source to the integer point $(n, n+3)$, not counting the extremes. Show that: $$
f(n)=\left\{\begin{array}{lll}
2 & \text{ if } & n \text{ is multiple of } 3 \\
0 & \text{ if } & n \text{ is not a multiple of } 3 .
\end{array}\right.
$$
f(n)=\left\{\begin{array}{lll}
2 & \text{ if } & n \text{ is multiple of } 3 \\
0 & \text{ if } & n \text{ is not a multiple of } 3 .
\end{array}\right.
$$