Erdős Problem 190

### What is the conjecture

https://www.erdosproblems.com/190

Let $H(k)$ be the smallest $N$ such that in any finite colouring of $\\{1,\ldots,N\\}$ (into any number of colours) there is always either a monochromatic $k$-term arithmetic progression or a rainbow arithmetic progression (i.e. all elements are different colours). Estimate $H(k)$. Is it true that
$$H(k)^{1/k}/k \to \infty$$
as $k\to\infty$?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else