TERAI'S CONJECTURE ON EXPONENTIAL DIOPHANTINE EQUATIONS

DOI10.1142/S1793042111004496zbMath1221.11092WikidataQ123290193 ScholiaQ123290193MaRDI QIDQ5198400

Takafumi Miyazaki

Publication date: 8 August 2011

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

zbMATH Keywords

Jacobi symbolexponential Diophantine equationsgeneralized Fermat equationsTerrai's conjecture

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

Related Items (8)

Exceptional cases of Terai's conjecture on Diophantine equations ⋮ On the exponential Diophantine equation \((3pm^2-1)^x + ( p( p - 3)m^2 + 1)^y = (pm)^z\) ⋮ On the exponential Diophantine equation $(n-1)^{x}+(n+2)^{y}=n^{z}$ ⋮ The exponential Diophantine equation \(\left(4 m^2 + 1\right)^x + \left(5 m^2 - 1\right)^y = (3 m)^z\) ⋮ On the Diophantine equation (( c + 1) m 2 + 1) x + ( cm 2 ⋮ On the Diophantine equation $(5pn^{2}-1)^{x}+(p(p-5)n^{2}+1)^{y}=(pn)^{z}$ ⋮ ON THE EXPONENTIAL DIOPHANTINE EQUATION ⋮ On the system of Diophantine equations \((m^2 - 1)^r + b^2 = c^2\) and \((m^2 - 1)^x + b^y = c^z\)

Uses Software

• ecdata

Cites Work

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• Ternary Diophantine Equations via Galois Representations and Modular Forms
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• Sur les équations x^p+2^βy^p= z²et x^p+2^βy^p= 2z²
• On the Equations z^m = F (x, y ) and Ax^p + By^q = Cz^r

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