MathDB

Suppose

s,k,t\in \mathbb N

. We've colored each natural number with one of the

k

colors, such that each color is used infinitely many times. We want to choose a subset

\mathcal A

\mathbb N

such that it has

t

disjoint monochromatic

s

-element subsets. What is the minimum number of elements of

A

?
Proposed by Navid Adham

Problem Statement