Find the smallest h(d) such that the following holds. There exists a function f:N→-1,1 such that, for every d≥ 1, max_P_d| ∑_n∈ P_df(n)|≤ h(d), where P_d ranges over all finite arithmetic progressions with common difference d.

Erdős Problem #177 — Find the smallest $h(d)$ such that the following holds.

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 $d$ .