Skip to content

Erdős problem 296

Start work

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)?

How the state got here

1 of 6 recorded
  1. Prior stateNone retained
  2. WorkNo submitted work retained
  3. VerificationNo check retained
  4. DecisionNo Repository has decided
  5. StandingA Result stands here
  6. Next gapNot recorded

Result history

Published changes, performers, checks, and later corrections.

No result history yet
No proposed change is retained for this Problem, so there is nothing to show a decision on.

Correction history

No correction history

Technical detailsExact roots, source, and retained record identifiers

Exact provenance

Problem row
sha256:4546743cdf44df6216964359b7fab83d43a9affaa20e65870053ba9b597c3015
Metadata
sha256:ee8db320c5a505175ecaf960c5dab49586dc25c099bbaf17ebccae1bf6ecb596
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:883936c8b983206c7e6a0ac2b0b3524242898298e07b77b5e0fdcf5979e5b584
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
Upstream sourceInspect recordsSource JSON