Erdős Problem #302

declared status 'open'. Formalized: no. Let $f(N)$ be the size of the largest $A\subseteq \{1,\ldots,N\}$ such that there are no solutions to$$\frac{1}{a}= \frac{1}{b}+\frac{1}{c}$$with distinct $a,b,c\in A$? Estimate $f(N)$. In particular, is $f(N)=(\tfrac{1}{2}+o(1))N$? Prize: no. OEIS: A390395. Tags: number theory, unit fractions.

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