On the Diophantine equation \(\frac{x^3-1}{x-1}=\frac{y^n-1}{y-1}\)

DOI10.1016/j.jnt.2004.12.002zbMath1063.11009OpenAlexW2006559454MaRDI QIDQ1775568

Pingzhi Yuan

Publication date: 4 May 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.12.002

zbMATH Keywords

exponential Diophantine equationsquadratic equations

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

Related Items

An old and new approach to Goormaghtigh’s equation ⋮ On the number of solutions of Goormaghtigh equation for given \(x\) and \(y\) ⋮ Unnamed Item ⋮ On the Diophantine equation \(ax^2+by^2=ck^n\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The diophantine equation \(x^2+7=2^n\)
• On the Diophantine equation \(\frac{x^m-1}{x-1}=\frac{y^n-1}{y-1}\).
• On the number of solutions of the generalized Ramanujan-Nagell equation
• Existence of primitive divisors of Lucas and Lehmer numbers
• Exceptional solutions of the exponential diophantine equation (x3 - 1) / (x - 1) = (yn - 1) / (y - 1)
• Integers with identical digits
• On the equation $a(x^m-1)/(x-1)=b(y^n-1)/(y-1)$.
• On the diophantine equation $(x^3-1)/(x-1)=(y^n-1)/(y-1)$
• On an equation of Goormaghtigh
• The Diophantine equation 2𝑥²+1=3ⁿ
• EQUATIONS OF THE FORM f(x)=g(y)