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Erdős problem 296

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Let N≥1N\geq 1 and let k(N)k(N) be maximal such that there are kk disjoint A1,…,Ak⊆{1,…,N}A_1,\ldots,A_k\subseteq \{1,\ldots,N\} with ∑n∈Ai1n=1\sum_{n\in A_i}\frac{1}{n}=1 for all ii. Estimate k(N)k(N). Is it true that k(N)=o(log⁡N)k(N)=o(\log N)?

Erdős Problems records this as proved (Lean).

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  1. Sourceerdos-problems
  2. StatementRetained
  3. Formal1 retained
  4. Resolutionproved (Lean)
  5. WorkNone recorded
  6. DecisionNone here
  7. The questionNot reached
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Number Theory576Unit Fractions48
Erdős problem 321accepted
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