Given two points $P$ and $Q$ with both integer coordinates (lattice points), we say that $P$see the point $Q$ if the segment $PQ$ contains no other lattice points. An n-loop is a sequence of n points $P_1, P_2, ..., P_n$, each of which is a lattice point, such that the following conditions are met:
a) $P_i$ sees $P_i+1$ for every $1 \leq i \leq n-1$ and $P_n$ sees $P_1$;
b) No $P_i$ sees any other Pj , except those mentioned in item a);
c) There are no three collinear points. Determine if there is a 100-loop.
I was trying to force an arithmetic progression between the coordinates of three points to try to arrive at an absurdity, but I didn't get anything useful.