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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 
@article{10_4064_cm139_1_7,
     author = {Jianping Wang and Tingting Wang and Wenpeng Zhang},
     title = {A note on the exponential {Diophantine} equation $(4m^2+1)^x+(5m^2-1)^y=(3m)^z$},
     journal = {Colloquium Mathematicum},
     pages = {121--126},
     publisher = {mathdoc},
     volume = {139},
     number = {1},
     year = {2015},
     doi = {10.4064/cm139-1-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm139-1-7/}
}
TY  - JOUR
AU  - Jianping Wang
AU  - Tingting Wang
AU  - Wenpeng Zhang
TI  - A note on the exponential Diophantine equation $(4m^2+1)^x+(5m^2-1)^y=(3m)^z$
JO  - Colloquium Mathematicum
PY  - 2015
SP  - 121
EP  - 126
VL  - 139
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm139-1-7/
DO  - 10.4064/cm139-1-7
LA  - en
ID  - 10_4064_cm139_1_7
ER  - 
%0 Journal Article
%A Jianping Wang
%A Tingting Wang
%A Wenpeng Zhang
%T A note on the exponential Diophantine equation $(4m^2+1)^x+(5m^2-1)^y=(3m)^z$
%J Colloquium Mathematicum
%D 2015
%P 121-126
%V 139
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm139-1-7/
%R 10.4064/cm139-1-7
%G en
%F 10_4064_cm139_1_7
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. http://geodesic.mathdoc.fr/articles/10.4064/cm139-1-7/

Cité par Sources :