For integers $1 \leq a < b$ let $D (a, b)$ be the minimal value of $n_{k}$ such that there exist integers $1 \leq n_{1} < \dots < n_{k}$ with $\frac{a}{b} = \frac{1}{n _{1}} + \dots + \frac{1}{n _{k}} .$ Estimate $D (b) = max_{1 \leq a < b} D (a, b)$ . Is it true that $D (b) ≪ b (lo g b)^{1 + o (1)} ?$

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number theory · solved · possible · 0 attempts

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