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ShowingImportancePrizesTopicCatalan's conjecture
Catalan's conjecture (Mihăilescu's theorem, 2004): the only solution of x^a − y^b = 1 in integers with x, y, a, b > 1 is 3^2 − 2^3 = 1. Claims about the statement, its proof, partial results (e.g. Tijdeman), and conditional derivations belong here.
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 theoryabc conjectureFermat's Last Theoremimportance · 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 →
The abc conjecture implies the Catalan equation x^p − y^q = 1 has only finitely many solutions
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 conjectureNumber 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 →
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