MathDB

Find all integers

n

greater than or equal to

4

that satisfy the following conditions:
[*] Take an arbitrary convex

n

-gon

P

on the coordinate plane whose vertices are lattice points (points whose coordinates are both integers). There are a total of

n

triangles that share two sides with

P

. Let

S_1, S_2, \ldots, S_n

be their areas, and let

S

be the area of

P

. Then, the greatest common divisor of

2S_1, 2S_2, \ldots, 2S_n

divides the integer

2S

Problem Statement