Sur l'équation {$a\sp 3+b\sp 3=c\sp p$}
Kraus, Alain
Experiment. Math., Tome 7 (1998) no. 4, p. 1-13 / Harvested from Project Euclid
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Let $p$ be a prime number $\geq 17$. This paper deals with the diophantine equation $a^3+b^3=c^p$. If we suppose that the Taniyama-Weil conjecture is true, we get a criterion that often allows one to prove that this equation has no nonzero integer solution with $a$, $b$ and $c$ coprime. In particular, we verify that this is the case if $p$ is < 10000.
Publié le : 1998-05-14
Classification:  11D41,  11F11,  11F30,  11G05,  11G20 
@article{1047674269,
     author = {Kraus, Alain},
     title = {Sur l'\'equation {$a\sp 3+b\sp 3=c\sp p$}},
     journal = {Experiment. Math.},
     volume = {7},
     number = {4},
     year = {1998},
     pages = { 1-13},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/1047674269}
}

Kraus, Alain. Sur l'équation {$a\sp 3+b\sp 3=c\sp p$}. Experiment. Math., Tome 7 (1998) no. 4, pp.  1-13. http://gdmltest.u-ga.fr/item/1047674269/