On the system of Diophantine equations a2+b2=(m2+1)rand ax+by=(m2+1)z

DOI10.4064/AA153-4-3zbMath1272.11047OpenAlexW2561528377MaRDI QIDQ2883257

Florian Luca

Publication date: 11 May 2012

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

Full work available at URL: https://doi.org/10.4064/aa153-4-3

zbMATH Keywords

exponential Diophantine equationTerai's conjectureGel'fond-Baker method

Mathematics Subject Classification ID

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

Related Items (6)

A purely exponential Diophantine equation in three unknowns ⋮ An upper bound for the number of solutions of ternary purely exponential Diophantine equations ⋮ On the exponential Diophantine equation \((am^2 + 1)^x + (bm^2 - 1)^y= (cm)^z\) with \(c \mid m\) ⋮ The exponential Diophantine equation \(\left(4 m^2 + 1\right)^x + \left(5 m^2 - 1\right)^y = (3 m)^z\) ⋮ Number of solutions to a special type of unit equations in two unknowns, II ⋮ On the system of Diophantine equations \((m^2 - 1)^r + b^2 = c^2\) and \((m^2 - 1)^x + b^y = c^z\)

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