A bound for the solutions of the Diophantine equation $D_1 x^2 + D_2^m = 4y^n$

Cipu, Mihai

Cipu, Mihai

Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, p. 179-180 / Harvested from Project Euclid

Résumé

We show that in every solutions $(D_1,D_2,x,y,m,n)$ of the equation $D_1 x^2 + D_2^m = 4 y^n$ with $n$ prime and coprime with the class-number of the imaginary quadratic field $\mathbf{Q}(\sqrt{-D_1D_2})$ one has $n \leq 5351$.

Publié le : 2002-12-14
Classification: Generalized Ramanujan equation, linear forms in logarithms, 11D61

@article{1148392266,
     author = {Cipu, Mihai},
     title = {A bound for the solutions of the Diophantine equation $D\_1 x^2 + D\_2^m = 4y^n$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {78},
     number = {10},
     year = {2002},
     pages = { 179-180},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148392266}
}

Cipu, Mihai. A bound for the solutions of the Diophantine equation $D_1 x^2 + D_2^m = 4y^n$. Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, pp.  179-180. http://gdmltest.u-ga.fr/item/1148392266/