MathDB

In the coordinate plane consider the set

S

of all points with integer coordinates. For a positive integer

k

, two distinct points

A

B\in S

will be called

k

-friends if there is a point

C\in S

such that the area of the triangle

ABC

is equal to

k

. A set

T\subset S

will be called

k

-clique if every two points in

T

are

k

-friends. Find the least positive integer

k

for which there exits a

k

-clique with more than 200 elements.
Proposed by Jorge Tipe, Peru

Problem Statement