ON THE EXPONENTIAL DIOPHANTINE EQUATION

DOI10.1017/S0004972713000956zbMath1334.11019MaRDI QIDQ5495454

Nobuhiro Terai, Takafumi Miyazaki

Publication date: 4 August 2014

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

exponential Diophantine equationinteger solutionlower bound for linear forms in two logarithms

Mathematics Subject Classification ID

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

Related Items (8)

An upper bound for the number of solutions of ternary purely exponential Diophantine equations ⋮ A parametric family of ternary purely exponential Diophantine equation $A^x+B^y=C^z$ ⋮ On the exponential Diophantine equation \((am^2 + 1)^x + (bm^2 - 1)^y= (cm)^z\) with \(c \mid m\) ⋮ On the exponential Diophantine equation \((3pm^2-1)^x + ( p( p - 3)m^2 + 1)^y = (pm)^z\) ⋮ Unnamed Item ⋮ On the Diophantine equation (( c + 1) m 2 + 1) x + ( cm 2 ⋮ On the Diophantine equation $(5pn^{2}-1)^{x}+(p(p-5)n^{2}+1)^{y}=(pn)^{z}$ ⋮ A note on the exponential Diophantine equation \((rlm^2-1)^x+(r(r-l)m^2+1)^y=(rm)^z\)

Cites Work

• Exceptional cases of Terai's conjecture on Diophantine equations
• Sur une classe d'équations exponentielles
• The diophantine equation \(a^ x+b^ y=c^ z\)
• On Some Exponential Equations of S. S. Pillai
• THE DIOPHANTINE EQUATION (2am - 1)^x + (2m)^y = (2am + 1)^z
• THE EXPONENTIAL DIOPHANTINE EQUATION n^x + (n + 1)^y = (n + 2)^z REVISITED
• Linear forms in two logarithms and interpolation determinants II
• An application of a lower bound for linear forms in two logarithms to the Terai–Jeśmanowicz conjecture
• Linear forms in p-adic logarithms and the Diophantine equation formula here
• TERAI'S CONJECTURE ON EXPONENTIAL DIOPHANTINE EQUATIONS

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