Colouring the smooth numbers

Abstract: For a given $n$, can we colour the positive integers using precisely $n$ colours in such a way that for any $a$, the numbers $a, 2a, \dots, na$ all get different colours? This question is still open in general. I will present a survey of known results and some other problems it leads to.

This is joint work with Andros Caicedo and Thomas Chartier.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)