Skip to content

Erdős problem 12

Let A⊂NA \subset \mathbb{N} be infinite with no distinct a,b,c∈Aa, b, c \in A such that a∣(b+c)a \mid (b + c) with b,c>ab, c > a. Can ∣A∩[1,N]∣/N|A \cap [1, N]|/\sqrt{N} have positive lower limit? Must every such AA fall below N1−cN^{1-c} infinitely often?

Workspace

Continue locallyOpen sourceSign in to contribute

Open this exact Problem, source revision, and authority Repository in Workbench. This handoff does not clone, switch, upload, or execute anything.

Canvas

public preview
  1. Source#12
  2. ResultNone
  3. Checks0

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

  • AI building on literature

    Erdős AI contributions wiki · 7 Apr, 2026

    Machine
    DeepMind prover agent
    Open the source record

  • AI collaborating with humans

    Erdős AI contributions wiki · 7 Apr, 2026

    Machine
    GPT-5.4 Thinking
    People
    Nat Sothanaphan, Terence Tao
    Open the source record

  • argument

    VibeMathed

    Machine
    AlphaProof Nexus
    Reported outcome
    partial
    Open the source record

Search problems.science

Find a Problem, Result, source, or page