THE DIOPHANTINE EQUATION (2am - 1)x + (2m)y = (2am + 1)z

DOI10.1142/S1793042112501151zbMath1290.11068OpenAlexW2064096040MaRDI QIDQ3165315

Takafumi Miyazaki, Alain S. Togbé

Publication date: 26 October 2012

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

Full work available at URL: https://doi.org/10.1142/s1793042112501151

zbMATH Keywords

exponential Diophantine equations

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items (9)

On the Diophantine equation \(a^x+b^y=(a+2)^z\) ⋮ 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 \(c \mid m\) ⋮ On the exponential Diophantine equation $(n-1)^{x}+(n+2)^{y}=n^{z}$ ⋮ The exponential Diophantine equation \(\left(4 m^2 + 1\right)^x + \left(5 m^2 - 1\right)^y = (3 m)^z\) ⋮ Jeśmanowicz' conjecture with Fermat numbers ⋮ The Diophantine equation (m2 + n2)x + (2mn)y = (m + n)2z ⋮ ON THE EXPONENTIAL DIOPHANTINE EQUATION ⋮ JEŚMANOWICZ’ CONJECTURE REVISITED

Cites Work

• The diophantine equation \(x^ 2 + 2^ k = y^ n\)
• On Cohn's conjecture concerning the Diophantine equation \(x^2+2^m=y^n\)
• Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation
• THE EXPONENTIAL DIOPHANTINE EQUATION n^x + (n + 1)^y = (n + 2)^z REVISITED
• Linear forms in two logarithms and interpolation determinants II
• Sur les équations x^p+2^βy^p= z²et x^p+2^βy^p= 2z²

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