Problem 3

Erdős Problem #3: declared status 'open'. Formalized: yes. If $A\subseteq \mathbb{N}$ has $\sum_{n\in A}\frac{1}{n}=\infty$ then must $A$ contain arbitrarily long arithmetic progressions? Prize: $5000. OEIS: A003002, A003003, A003004, A003005. Tags: additive combinatorics, arithmetic progressions, number theory.