Number of solutions to \(ka^x+lb^y=c^z\)

DOI10.1016/j.jnt.2017.10.031zbMath1430.11046OpenAlexW2772676005MaRDI QIDQ1747225

Pingzhi Yuan, Wenyu Luo, Naijuan Deng

Publication date: 4 May 2018

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2017.10.031

zbMATH Keywords

exponential Diophantine equation

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items (1)

On the exponential Diophantine equation $(n-1)^{x}+(n+2)^{y}=n^{z}$

Cites Work

• Unnamed Item
• The generalized Pillai equation \(\pm ra^x\pm sb^y=c\)
• On the equations \(p^x - b^y = c\) and \(a^x + b^y = c^z\)
• On the generalized Pillai equation \(\pm a^{x}\pm b^{y}=c\)
• A note on the diophantine equation \(ax^ m - by^ n = k\)
• The diophantine equation \(a^ x+b^ y=c^ z\)
• On \(p^x-q^y=c\) and related three term exponential Diophantine equations with prime bases.
• An upper bound for the number of solutions of ternary purely exponential Diophantine equations
• Zur Approximation algebraischer Zahlen. I: Über den grössten Primteiler binärer Formen
• The number of solutions to the generalized Pillai equation \(\pm ra^{x} \pm sb^{y}=c\).
• On the Diophantine equation \(ax^2+by^2=ck^n\)
• On the number of solutions of the generalized Ramanujan-Nagell equation
• Existence of primitive divisors of Lucas and Lehmer numbers
• On Some Exponential Equations of S. S. Pillai
• Jeśmanowicz’ Conjecture with Congruence Relations. II
• Handling a large bound for a problem on the generalized Pillai equation $\pm r a^x \pm s b^y = c$
• Number of solutions to $a^x + b^y = c^z$
• The equation x+y=1 in finitely generated groups
• ON THE NUMBER OF SOLUTIONS OF THE DIOPHANTINE EQUATIONax^m−byⁿ=c
• Primitive Divisors of Lucas and Lehmer Sequences

This page was built for publication: Number of solutions to \(ka^x+lb^y=c^z\)