MathDB

Let

n>2

be an integer

.

We want to color in red exactly

n+1

of the numbers

1,2,\cdots,2n-1, 2n

so that there do not exists three distinct red integers

x,y,z

satisfying

x+y=z.

Prove that there is one and one only way to color the red numbers according to the given condition

.

Problem Statement