On the exponential Diophantine equation \((am^2 + 1)^x + (bm^2 - 1)^y= (cm)^z\) with \(c \mid m\)

DOI10.1007/s10998-016-0170-zzbMath1413.11073OpenAlexW2563481238MaRDI QIDQ1705214

Ruiqin Fu, Hai Yang

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

zbMATH Keywords

exponential Diophantine equationapplication of BHV theoremexistence of primitive divisor of Lucas and Lehmer numbers

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

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

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• A note on the exponential Diophantine equation (4m²+1)^x+(5m²-1)^y=(3m)^z
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