Determine all integers
![n > 3](/media/m/4/6/2/462be2e53641b265006847e06a169c39.png)
for which there exist
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
points
![A_{1},\cdots ,A_{n}](/media/m/9/b/9/9b966ad49b418c0b4b5cef19a0fb6f49.png)
in the plane, no three collinear, and real numbers
![r_{1},\cdots ,r_{n}](/media/m/f/b/5/fb59d4d412234020a8ac89663a7335fb.png)
such that for
![1\leq i < j < k\leq n](/media/m/a/d/0/ad0e299377ea39d9d4a88c6e550853aa.png)
, the area of
![\triangle A_{i}A_{j}A_{k}](/media/m/6/b/d/6bd980c06e1459cf0fdf46237c53bf4a.png)
is
![r_{i} + r_{j} + r_{k}](/media/m/f/1/0/f10ad234360fb2b4a867f09d8f9d8dc5.png)
.
%V0
Determine all integers $n > 3$ for which there exist $n$ points $A_{1},\cdots ,A_{n}$ in the plane, no three collinear, and real numbers $r_{1},\cdots ,r_{n}$ such that for $1\leq i < j < k\leq n$, the area of $\triangle A_{i}A_{j}A_{k}$ is $r_{i} + r_{j} + r_{k}$.