Let
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
be a set of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
points in the plane
![(n \geq 3)](/media/m/0/5/f/05f84f639d78a8813cd23e7bebb55e38.png)
whose coordinates are integers such that any three points from
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
are vertices of a nondegenerate triangle whose centroid doesnt have both coordinates integers. Determine the maximal
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Let $E$ be a set of $n$ points in the plane $(n \geq 3)$ whose coordinates are integers such that any three points from $E$ are vertices of a nondegenerate triangle whose centroid doesnt have both coordinates integers. Determine the maximal $n.$