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KindShowingImportancePrizesTopicCatalan'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.
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 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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