MathDB

Each of the numbers in the set

N = \{1, 2, 3, \cdots, n - 1\}

, where

n \geq 3

, is colored with one of two colors, say red or black, so that:
(i)

i

and

n - i

always receive the same color, and
(ii) for some

j \in N

, relatively prime to

n

i

and

|j - i|

receive the same color for all

i \in N, i \neq j.

Prove that all numbers in

N

must receive the same color.

Problem Statement