On the Diophantine equation |𝑎𝑥ⁿ-𝑏𝑦ⁿ|=1

DOI10.1090/S0025-5718-98-00900-4zbMath0892.11041OpenAlexW2131201676MaRDI QIDQ4372707

Michael A. Bennett, Benjamin M. M. de Weger

Publication date: 16 December 1997

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-98-00900-4

zbMATH Keywords

hypergeometric functionslinear forms in logarithmshigher degree diophantine equations

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Higher degree equations; Fermat's equation (11D41)

Related Items (11)

On integers with identical digits ⋮ Simplifying method for algebraic approximation of certain algebraic numbers ⋮ Diagonalizable Thue equations: revisited ⋮ On algebraic approximations of certain algebraic numbers. ⋮ Effective irrationality measures for real and p-adic roots of rational numbers close to 1, with an application to parametric families of Thue–Mahler equations ⋮ On the representation of unity by binary cubic forms ⋮ On unit power integral bases of \(\mathbb Z[\root 4 \of {m}\)] ⋮ Diagonalizable quartic Thue equations with negative discriminant ⋮ Thue's inequalities and the hypergeometric method ⋮ Solving Thue equations without the full unit group ⋮ On the Diophantine equations \(\binom n2=cx^l\) and \(\binom n3=cx^l\).

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