Catalan's Conjecture

DOI10.2307/2974663zbMath0866.11027OpenAlexW4239432560WikidataQ123112614 ScholiaQ123112614MaRDI QIDQ5285120

Paulo Ribenboim

Publication date: 20 July 1997

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2974663

zbMATH Keywords

Catalan's conjectureconsecutive integersconsecutive powershigher degree diophantine equations

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

Related Items (13)

A class number free criterion for Catalan's conjecture. ⋮ Large 2-transitive arcs ⋮ New bounds and conditions for the equation of Nagell-Ljunggren ⋮ On commoner's liveness theorem and supervisory policies that enforce liveness in free-choice Petri nets ⋮ Class Number Conditions for the Diagonal Case of the Equation of Nagell and Ljunggren ⋮ An elementary solution of the Diophantine equation \(x^3=y^2-1\) ⋮ On the number of solutions of the generalized Ramanujan-Nagell equation ⋮ Affine planes admitting a collineation group with a transitive action on the line at infinity ⋮ On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation ⋮ On simple \(K_4\)-groups ⋮ Improved lower bounds for possible solutions in the second case of the Fermat last theorem and in the Catalan equation ⋮ On the Diophantine equations \(\binom n2=cx^l\) and \(\binom n3=cx^l\). ⋮ Pillai's conjecture revisited.

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