Question 4
A colouring of $\mathbb{Q}$ consists of colouring every rational number either red or blue. A colouring of $\mathbb{Q}$ is called harmonious if, for all rationals $x$ and $y$ of the same colour, the rational $x+y$ also has that same colour.
Find all colourings of $\mathbb{Q}$ that are harmonious.
Find all colourings of $\mathbb{Q}$ that are harmonious.