On the exponential Diophantine equation \((am^2 + 1)^x + (bm^2 - 1)^y= (cm)^z\) with \(c \mid m\)
From MaRDI portal
Publication:1705214
DOI10.1007/s10998-016-0170-zzbMath1413.11073OpenAlexW2563481238MaRDI QIDQ1705214
Publication date: 14 March 2018
Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10998-016-0170-z
exponential Diophantine equationapplication of BHV theoremexistence of primitive divisor of Lucas and Lehmer numbers
Related Items (7)
Unnamed Item ⋮ A parametric family of ternary purely exponential Diophantine equation $A^x+B^y=C^z$ ⋮ On the exponential Diophantine equation \((m^2+m+1)^x+m^y=(m+1)^z\) ⋮ 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 ⋮ On the Diophantine equation $(5pn^{2}-1)^{x}+(p(p-5)n^{2}+1)^{y}=(pn)^{z}$ ⋮ A note on the exponential Diophantine equation \((rlm^2-1)^x+(r(r-l)m^2+1)^y=(rm)^z\)
Cites Work
- Unnamed Item
- Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples. II
- On Jeśmanowicz' conjecture concerning primitive Pythagorean triples
- Some exponential diophantine equations. I: The equation \(D_1x^2 - D_2y^2 = \lambda k^z\)
- Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples
- A note on Jeśmanowicz' conjecture concerning primitive Pythagorean triples
- On the number of solutions of the generalized Ramanujan-Nagell equation
- Existence of primitive divisors of Lucas and Lehmer numbers
- On the system of Diophantine equations a2+b2=(m2+1)rand ax+by=(m2+1)z
- THE DIOPHANTINE EQUATION (2am - 1)x + (2m)y = (2am + 1)z
- Primitive Divisors of Lucas and Lehmer Sequences
- A note on the exponential Diophantine equation (4m2+1)x+(5m2-1)y=(3m)z
- On a pure ternary exponential Diophantine equation
- On Square Fibonacci Numbers
- A note on the article by F. Luca ``On the system of Diophantine equations a2+b2=(m2+1)rand ax+by=(m2+1)z (Acta Arith. 153 (2012), 373–392)
- ON THE EXPONENTIAL DIOPHANTINE EQUATION
This page was built for publication: On the exponential Diophantine equation \((am^2 + 1)^x + (bm^2 - 1)^y= (cm)^z\) with \(c \mid m\)
