A note on the exponential Diophantine equation \((rlm^2-1)^x+(r(r-l)m^2+1)^y=(rm)^z\)

DOI10.1007/S00574-022-00314-8zbMath1502.11037OpenAlexW4298138611WikidataQ115606461 ScholiaQ115606461MaRDI QIDQ2091205

Shuanglin Fei, Jiagui Luo

Publication date: 31 October 2022

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-022-00314-8

zbMATH Keywords

exponential Diophantine equationgeneralized Ramanujan-Nagell equationslinear forms in \(p\)-adic logarithmsprimitive divisors of Lucas sequences

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the exponential Diophantine equation \((am^2 + 1)^x + (bm^2 - 1)^y= (cm)^z\) with \(c \mid m\)
• On the exponential Diophantine equation \((3pm^2-1)^x + ( p( p - 3)m^2 + 1)^y = (pm)^z\)
• The exponential Diophantine equation \(\left(4 m^2 + 1\right)^x + \left(5 m^2 - 1\right)^y = (3 m)^z\)
• Some exponential diophantine equations. I: The equation \(D_1x^2 - D_2y^2 = \lambda k^z\)
• On the exponential Diophantine equation \((m^2+m+1)^x+m^y=(m+1)^z\)
• The complete solution of the Diophantine equation \((4m^2 + 1)^x + (5m^2 - 1)^y = (3m)^z\)
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• On the number of solutions of the generalized Ramanujan-Nagell equation
• Existence of primitive divisors of Lucas and Lehmer numbers
• On Some Exponential Equations of S. S. Pillai
• A Hasse-type principle for exponential Diophantine equations and its applications
• Linear forms in p-adic logarithms and the Diophantine equation formula here
• A note on the exponential Diophantine equation (4m²+1)^x+(5m²-1)^y=(3m)^z
• A parametric family of ternary purely exponential Diophantine equation $A^x+B^y=C^z$
• On the Diophantine equation $(5pn^{2}-1)^{x}+(p(p-5)n^{2}+1)^{y}=(pn)^{z}$
• A note on the ternary purely exponential diophantine equation Ax + By = Cz with A + B = C2
• A Survey on the Ternary Purely Exponential Diophantine Equation $a^x + b^y = c^z$
• A note on the exponential diophantine equation $(am^2+1)^x+(bm^2-1)^y=(cm)^z$
• ON THE EXPONENTIAL DIOPHANTINE EQUATION
• On the exponential Diophantine equation (18m2 + 1)x + (7m2 -1)y = (5m)z
• On the Diophantine equation (( c + 1) m 2 + 1) x + ( cm 2

This page was built for publication: A note on the exponential Diophantine equation \((rlm^2-1)^x+(r(r-l)m^2+1)^y=(rm)^z\)