Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples

DOI10.1016/j.jnt.2012.08.018zbMath1309.11029OpenAlexW4206104890WikidataQ114157585 ScholiaQ114157585MaRDI QIDQ1930116

Takafumi Miyazaki

Publication date: 10 January 2013

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.08.018

zbMATH Keywords

Pythagorean triplesexponential Diophantine equationsJeśmanowicz' conjecture

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41) Linear forms in logarithms; Baker's method (11J86)

Related Items (20)

On the exceptional solutions of Jeśmanowicz' conjecture ⋮ 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 ⋮ Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples. II ⋮ On Jeśmanowicz' conjecture concerning primitive Pythagorean triples ⋮ On the exponential Diophantine equation \((am^2 + 1)^x + (bm^2 - 1)^y= (cm)^z\) with \(c \mid m\) ⋮ On the exponential Diophantine equation \((3pm^2-1)^x + ( p( p - 3)m^2 + 1)^y = (pm)^z\) ⋮ On the exponential Diophantine equation \((m^2+m+1)^x+m^y=(m+1)^z\) ⋮ A NOTE ON JEŚMANOWICZ’ CONJECTURE CONCERNING PRIMITIVE PYTHAGOREAN TRIPLES ⋮ The exponential Diophantine equation \(\left(4 m^2 + 1\right)^x + \left(5 m^2 - 1\right)^y = (3 m)^z\) ⋮ A NOTE ON THE DIOPHANTINE EQUATION ⋮ A note on Jeśmanowicz' conjecture concerning primitive Pythagorean triples. II. ⋮ Jeśmanowicz' conjecture with Fermat numbers ⋮ On Jeśmanowicz' conjecture concerning primitive Pythagorean triples. II ⋮ On the exponential Diophantine equation (18m2 + 1)x + (7m2 -1)y = (5m)z ⋮ A remark on Jeśmanowicz' conjecture for the non-coprimality case ⋮ The Diophantine equation (m2 + n2)x + (2mn)y = (m + n)2z ⋮ JEŚMANOWICZ’ CONJECTURE ON PYTHAGOREAN TRIPLES ⋮ JEŚMANOWICZ’ CONJECTURE REVISITED ⋮ A note on Jeśmanowicz' conjecture concerning primitive Pythagorean triples

Cites Work

• Jeśmanowicz' conjecture on exponential Diophantine equations
• On the equations \(p^x - b^y = c\) and \(a^x + b^y = c^z\)
• Sur une classe d'équations exponentielles
• On Some Exponential Equations of S. S. Pillai
• The equation x+y=1 in finitely generated groups
• THE EXPONENTIAL DIOPHANTINE EQUATION n^x + (n + 1)^y = (n + 2)^z REVISITED
• A note on Jeśmanowicz' conjecture concerning primitive Pythagorean triplets
• On the equation x³+y³=2z³
• Linear forms in two logarithms and interpolation determinants II
• ON THE CONJECTURE OF JEŚMANOWICZ CONCERNING PYTHAGOREAN TRIPLES
• On a conjecture on exponential Diophantine equations
• A corollary to a theorem of Laurent-Mignotte-Nesterenko
• A note on a conjecture of Jeśmanowicz
• Applications of a lower bound for linear forms in two logarithms to exponential Diophantine equations
• Number Theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples