Geodesic
On the Diophantine equation $x^2 + 2^{\alpha} 13^{\beta}= y^{n}$
Florian Luca 1   ; Alain Togbé 2
1 Instituto de Matemáticas UNAM Campus Morelia Apartado Postal 27-3 (Xangari) C.P. 58089 Morelia, Michoacán, Mexico
2 Mathematics Department Purdue University North Central 1401 S, U.S. 421 Westville, IN 46391 U.S.A.
Colloquium Mathematicum, Tome 116 (2009) no. 1, pp. 139-146 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We find all the solutions of the Diophantine equation $$x^2 + 2^{\alpha} 13^{\beta}= y^n$$ in positive integers $x,y,\alpha,\beta,n\ge 3$ with $x$ and $y$ coprime.
DOI : 10.4064/cm116-1-7
Mots-clés : solutions diophantine equation alpha beta positive integers alpha beta coprime

Florian Luca  1   ; Alain Togbé  2

1 Instituto de Matemáticas UNAM Campus Morelia Apartado Postal 27-3 (Xangari) C.P. 58089 Morelia, Michoacán, Mexico
2 Mathematics Department Purdue University North Central 1401 S, U.S. 421 Westville, IN 46391 U.S.A. 
@article{10_4064_cm116_1_7,
     author = {Florian Luca and Alain Togb\'e},
     title = {On the {Diophantine} equation $x^2 + 2^{\alpha} 13^{\beta}=
y^{n}$},
     journal = {Colloquium Mathematicum},
     pages = {139--146},
     year = {2009},
     volume = {116},
     number = {1},
     doi = {10.4064/cm116-1-7},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm116-1-7/}
}
TY  - JOUR
AU  - Florian Luca
AU  - Alain Togbé
TI  - On the Diophantine equation $x^2 + 2^{\alpha} 13^{\beta}=
y^{n}$
JO  - Colloquium Mathematicum
PY  - 2009
SP  - 139
EP  - 146
VL  - 116
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm116-1-7/
DO  - 10.4064/cm116-1-7
LA  - fr
ID  - 10_4064_cm116_1_7
ER  - 
%0 Journal Article
%A Florian Luca
%A Alain Togbé
%T On the Diophantine equation $x^2 + 2^{\alpha} 13^{\beta}=
y^{n}$
%J Colloquium Mathematicum
%D 2009
%P 139-146
%V 116
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm116-1-7/
%R 10.4064/cm116-1-7
%G fr
%F 10_4064_cm116_1_7
Florian Luca; Alain Togbé. On the Diophantine equation $x^2 + 2^{\alpha} 13^{\beta}=
y^{n}$. Colloquium Mathematicum, Tome 116 (2009) no. 1, pp. 139-146. doi: 10.4064/cm116-1-7

Cité par Sources :