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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.

SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.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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