Erdős Problem 177

### What is the conjecture

https://www.erdosproblems.com/177

Find the smallest $h(d)$ such that the following holds. There exists a function $f:\mathbb{N}\to\\{-1,1\\}$ such that, for every $d\geq 1$,

$$\max_{P_d}\left\lvert \sum_{n\in P_d}f(n)\right\rvert\leq h(d),$$
where $P_d$ ranges over all finite arithmetic progressions with common difference $d$.

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