Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples. II

DOI10.1016/J.JNT.2014.01.011zbMath1310.11040OpenAlexW1972898438WikidataQ114157543 ScholiaQ114157543MaRDI QIDQ402638

Pingzhi Yuan, Takafumi Miyazaki, Danyao Wu

Publication date: 28 August 2014

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2014.01.011

zbMATH Keywords

Pythagorean triplesexponential Diophantine equationsJeśmanowicz' conjecture

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

Related Items (11)

On the exceptional solutions of Jeśmanowicz' conjecture ⋮ 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 \((3pm^2-1)^x + ( p( p - 3)m^2 + 1)^y = (pm)^z\) ⋮ Unnamed Item ⋮ A NOTE ON JEŚMANOWICZ’ CONJECTURE CONCERNING PRIMITIVE PYTHAGOREAN TRIPLES ⋮ On Jeśmanowicz' conjecture concerning primitive Pythagorean triples. II ⋮ Jeśmanowicz' conjecture for polynomials ⋮ A remark on Jeśmanowicz' conjecture for the non-coprimality case ⋮ JEŚMANOWICZ’ CONJECTURE ON PYTHAGOREAN TRIPLES ⋮ On the system of Diophantine equations \((m^2 - 1)^r + b^2 = c^2\) and \((m^2 - 1)^x + b^y = c^z\)

Cites Work

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• Jeśmanowicz' conjecture on exponential Diophantine equations
• Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples
• Jeśmanowicz' conjecture with congruence relations
• Linear forms in two logarithms and interpolation determinants II
• A note on a conjecture of Jeśmanowicz

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