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3 claims

Fermat's Last Theorem: no positive integer solutions to x^n + y^n = z^n for n > 2. Claims about the theorem, its proof (Wiles–Taylor), conditional or alternative proofs, and reformulations belong here; general Diophantine questions without a connection to the theorem do not.

A proof of the abc conjecture would yield new proofs of Fermat's Last Theorem and Catalan's Conjecture.

SupportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Number theory abc conjecture Catalan's conjectureimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

Only an effective or explicit form of the abc conjecture yields a complete proof of Fermat's Last Theorem

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →abc conjecture Number theoryimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The abc conjecture implies Fermat's Last Theorem for all sufficiently large exponents

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