MathDB

Prove that, given a positive integrer

n

, there exists a positive integrer

k_n

with the following property: Given any

k_n

points in the space,

4

4

non-coplanar, and associated integrer numbers between

1

and

n

to each sharp edge that meets

2

of this points, there's necessairly a triangle determined by

3

of them, whose sharp edges have associated the same number.

Problem Statement