A conjecture concerning the pure exponential Diophantine equation \(a^x+b^y= c^z\)

DOI10.1007/s10114-004-0436-xzbMath1159.11308OpenAlexW2023522367WikidataQ123161670 ScholiaQ123161670MaRDI QIDQ2581228

Maohua Le

Publication date: 9 January 2006

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-004-0436-x

zbMATH Keywords

number of solutionsexponential Diophantine equationcomplete determination

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items (4)

A note on the exceptional solutions of Jeśmanowicz' conjecture concerning primitive Pythagorean triples ⋮ On the Terai-Jésmanowicz conjecture ⋮ On the Diophantine equation $(5pn^{2}-1)^{x}+(p(p-5)n^{2}+1)^{y}=(pn)^{z}$ ⋮ ON THE CONJECTURE OF JEŚMANOWICZ CONCERNING PYTHAGOREAN TRIPLES

Cites Work

• The diophantine equation \(a^ x+b^ y=c^ z\)
• Zur Approximation algebraischer Zahlen. I: Über den grössten Primteiler binärer Formen
• The diophantine equation \(a^ x + b^ y = c^ z\). III
• Existence of primitive divisors of Lucas and Lehmer numbers
• Some diophantine equations of the form $x^n + y^n = z^m$
• Applications of a lower bound for linear forms in two logarithms to exponential Diophantine equations
• A note on the Diophantine equation $a^x + b^y = c^z$
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