OPENNOTORIOUSnumber theoryadditive combinatoricsarithmetic progressions
If $A\subseteq \mathbb{N}$ has $\sum_{n\in A}\frac{1}{n}=\infty$ then must $A$ contain arbitrarily long arithmetic progressions?
Notes: The k=3 case was proved by Bloom and Sisask, with better bounds by Kelley and Meka. For general k, Leng, Sah, and Sawhney proved r_k(N) << N/exp((log log N)^{c_k}). This is one of the most famous open problems in combinatorics.
AI Status: NONE · 0 total attempts