Skip to published state

Erdős problem / erdos

open offer

Problem 488

Exact records and bounded producer offers matched to this problem.

Current bounded offer

rank 9
availableerdos:488
Erdős 488
Advance Erdős problem 488 from its pinned statement, theorem and proof records, attempts, residual obligations, dependency context, and source locks; produce one decision-relevant artifact or an informative negative result without repeating banked routes.
  1. Targeterdos:488
  2. Packetsite/problems/488.json
  3. Verifiererdos-frontier.problem-work.v1
Inspect ranked work
Exact offer contractPacket, root, and verifier profile
Verifier
erdos-frontier.problem-work.v1
Packet
site/problems/488.json
Packet root
sha256:b5ec2ddf11ee19e2ad4c7fd60e30ac604e7392670247060956565a9e5b4b6309

Matching finding records

1 records

  1. vf_bb045cbc56528d39

    theoretical

    Erdős Problem #488 [status: falsifiable; formalized: yes]. Let AA be a finite set andB={n≥1:a∣n for some a∈A}.B=\{ n \geq 1 : a\mid n\textrm{ for some }a\in A\}.Is it true that, for every m>n≥max⁡(A)m>n\geq \max(A),∣B∩[1,m]∣m<2∣B∩[1,n]∣n?\frac{\lvert B\cap [1,m]\rvert }{m}< 2\frac{\lvert B\cap [1,n]\rvert}{n}? Current best: The constant 22 would be the best possible here, as witnessed by taking A={a}A=\{a\}, n=2a−1n=2a-1, and m=2am=2a. Prize: no. Tags: number theory.

    recordedOpen record