Question 5
In a plane with cartesian coordinates, let $P$ and $Q$ be two regions of convex polygon (including boundary and interior) whose vertices are all integer points (i.e., their coordinates are all integers) and $T = P \cap Q$. Prove that if $T$ is not empty and does not contain integer point, then $T$ is a non-degenerate convex quadrilateral. (posed by Qu Zhenhua)