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The abc Conjecture

For every epsilon > 0, only finitely many coprime triples a + b = c satisfy c > rad(abc)^(1+epsilon).

5 statements · 4 links from papers · 0 composed · updated 2026-08-12 15:30:25.016641+00:00

Typed form: /api/frontier/abc-conjecture · the inclusive shelf of every claim is at /topics/abc-conjecture

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Derived, and unstated

Each of these follows from links two or more papers assert, but no paper in the corpus states it. A chain is only as strong as its weakest link, and the tier below reports that weakest link, not the best one.

  1. Nothing composes yet. That happens when the recorded links do not yet chain: a new paper reducing something to one of the classical criteria below is what starts it.

What would settle it

  1. No routes recorded yet.

What it would settle

  1. the target implies Irrationality of numbers such as log_A(2) is proven under the ABC conjecture.

    paper · stated · arxiv:2604.25566

  2. the target implies In certain special cases the explicit abc conjecture implies that the equation a1!!⋯at!!=n!! has only…

    paper · stated · arxiv:2604.09730

  3. the target implies It further obtains the stronger bound b ≫_ε a^{15/14 - ε} assuming the abc conjecture.

    paper · stated · arxiv:1906.11128

  4. the target implies only finitely many terms U_n in a nondegenerate Lucas sequence with Q = ±1 and positive discriminant Δ have…

    paper · stated · arxiv:2605.24909