A note on the equation $ax^n - by^n = c$

DOI10.4064/aa-75-3-287-295zbMath0861.11025OpenAlexW856757026MaRDI QIDQ4883037

Maurice Mignotte

Publication date: 12 May 1997

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/206878

zbMATH Keywords

exponential diophantine equationsexplicit lower boundlinear forms in two logarithms of algebraic numbersbinary form of degree \(\geq 3\)absolute upper bound for the degree \(n\)

Mathematics Subject Classification ID

Diophantine inequalities (11D75) Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

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Powers in recurrence sequences: Pell equations ⋮ On perfect powers that are sums of cubes of a seven term arithmetic progression ⋮ On power values of pyramidal numbers, II ⋮ 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 ⋮ The Diophantine equation \((x^{k} - 1)(y^{k} - 1) = (z^{k} - 1)^{t}\) ⋮ On the Diophantine equation |𝑎𝑥ⁿ-𝑏𝑦ⁿ|=1 ⋮ Thue's inequalities and the hypergeometric method ⋮ On the power values of power sums ⋮ Representation of integers by sparse binary forms ⋮ On the Diophantine equations \(\binom n2=cx^l\) and \(\binom n3=cx^l\). ⋮ Linear Forms in Logarithms

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