On the Diophantine equation \((x^ k-1)(y^ k-1)=(z^ k-1)\).

DOI10.1016/S0019-3577(04)90002-XzbMath1098.11022MaRDI QIDQ1890409

Yann Bugeaud

Publication date: 3 January 2005

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

zbMATH Keywords

exponential Diophantine equationlinear forms in two logarithms

Mathematics Subject Classification ID

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

Related Items (5)

The Diophantine equation \((ax^k-1)(by^k-1)=abz^k-1\) ⋮ On the Diophantine system \(f(z)= f(x) f(y)= f(u) f(v)\) ⋮ The Diophantine equation \((x^{k} - 1)(y^{k} - 1) = (z^{k} - 1)^{t}\) ⋮ On the Diophantine equation $f(x)f(y)=f(z)^n$ involving Laurent polynomials, II ⋮ Diophantine approximation and the equation \((a^2 c x^k - 1)(b^2 c y^k - 1) = (a b c z^k - 1)^2\)

Cites Work

• Unnamed Item
• Unnamed Item
• Linear forms in two logarithms and interpolation determinants
• Products of consecutive integers and the Markoff equation
• On a problem of Diophantus
• A corollary to a theorem of Laurent-Mignotte-Nesterenko
• There are only finitely many Diophantine quintuples
• On a problem of Diophantus for higher powers
• RATIONAL APPROXIMATIONS TO 23 AND OTHER ALGEBRAIC NUMBERS
• On products of consecutive integers

This page was built for publication: On the Diophantine equation \((x^ k-1)(y^ k-1)=(z^ k-1)\).