MathDB

Bijection exist?

Source: 2019 China TST Test 3 P3

March 23, 2019

Coloringbijectioncombinatorics

Problem Statement

Does there exist a bijection

f:\mathbb{N}^{+} \rightarrow \mathbb{N}^{+}

, such that there exist a positive integer

k

, and it's possible to have each positive integer colored by one of

k

chosen colors, such that for any

x \neq y

f(x)+y

and

f(y)+x

are not the same color?