Question 27
Prove that there exists a constant $\lambda \gt 0$, such that: for any positive integer $m$, in the rectangular coordinates system, if all vertices of $\triangle ABC$ are integral points, and there is a unique interior (not on the side) integral point whose $x$ and $y$ coordinates are multiples of $m$, then the area of $\triangle ABC$ is less than $\lambda m^3$.
(Contributed by Wang Bin and Fu Yunhao)
(Contributed by Wang Bin and Fu Yunhao)