Geodesic
A note on the exponential Diophantine equation $(4m^2+1)^x+(5m^2-1)^y=(3m)^z$
Jianping Wang1 ; Tingting Wang2 ; Wenpeng Zhang2
1 College of Science Chang'an University Xi'an, Shaanxi, P.R. China
2 Department of Mathematics Northwest University Xi'an, Shaanxi, P.R. China
Colloquium Mathematicum, Tome 139 (2015) no. 1, pp. 121-126 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $m$ be a positive integer. Using an upper bound for the solutions of generalized Ramanujan–Nagell equations given by Y. Bugeaud and T. N. Shorey, we prove that if $3\nmid m$, then the equation $(4m^2+1)^x+(5m^2-1)^y=(3m)^z$ has only the positive integer solution $(x,y,z)=(1,1,2)$.
DOI : 10.4064/cm139-1-7
Keywords: positive integer using upper bound solutions generalized ramanujan nagell equations given bugeaud shorey prove nmid equation has only positive integer solution

Jianping Wang 1 ; Tingting Wang 2 ; Wenpeng Zhang 2

1 College of Science Chang'an University Xi'an, Shaanxi, P.R. China
2 Department of Mathematics Northwest University Xi'an, Shaanxi, P.R. China 
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Jianping Wang; Tingting Wang; Wenpeng Zhang. A note on the exponential Diophantine equation $(4m^2+1)^x+(5m^2-1)^y=(3m)^z$. Colloquium Mathematicum, Tome 139 (2015) no. 1, pp. 121-126. doi: 10.4064/cm139-1-7

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