The Diophantine equation $Dx^2+2^{2m+1}=y^{n}$
Colloquium Mathematicum, Tome 98 (2003) no. 2, pp. 147-154
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
It is shown that for a given squarefree positive integer $D$, the equation of the title has no solutions in integers $x>0$, $m>0$, $n\ge 3$ and $y$ odd, nor unless $D\equiv 14 \ ({\rm mod}\hskip 1.7pt16)$ in integers $x>0$, $m=0$, $n\ge 3$, $y>0$, provided in each case that $n$ does not divide the class number of the imaginary quadratic field containing
$\sqrt {-2D}$, except for a small number of (stated) exceptions.
Keywords:
shown given squarefree positive integer equation title has solutions integers odd nor unless equiv mod hskip integers provided each does divide class number imaginary quadratic field containing sqrt except small number stated exceptions
Affiliations des auteurs :
J. H. E. Cohn 1
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author = {J. H. E. Cohn},
title = {The {Diophantine} equation $Dx^2+2^{2m+1}=y^{n}$},
journal = {Colloquium Mathematicum},
pages = {147--154},
publisher = {mathdoc},
volume = {98},
number = {2},
year = {2003},
doi = {10.4064/cm98-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm98-2-1/}
}
J. H. E. Cohn. The Diophantine equation $Dx^2+2^{2m+1}=y^{n}$. Colloquium Mathematicum, Tome 98 (2003) no. 2, pp. 147-154. doi: 10.4064/cm98-2-1
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