On generalized Fermat equations of signature (p,p,3)

Karolina Krawciów

Colloquium Mathematicae, Tome 122 (2011), p. 49-52 / Harvested from The Polish Digital Mathematics Library

Résumé

This paper focuses on the Diophantine equation $x ⁿ + p^{α} y ⁿ = M z ³$ , with fixed α, p, and M. We prove that, under certain conditions on M, this equation has no non-trivial integer solutions if $n \geq ℱ (M, p^{α})$ , where $ℱ (M, p^{α})$ is an effective constant. This generalizes Theorem 1.4 of the paper by Bennett, Vatsal and Yazdani [Compos. Math. 140 (2004), 1399-1416].

Publié le : 2011-01-01

Zbl 1252.11029

EUDML-ID : urn:eudml:doc:283919

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     author = {Karolina Krawci\'ow},
     title = {On generalized Fermat equations of signature (p,p,3)},
     journal = {Colloquium Mathematicae},
     volume = {122},
     year = {2011},
     pages = {49-52},
     zbl = {1252.11029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-4}
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Karolina Krawciów. On generalized Fermat equations of signature (p,p,3). Colloquium Mathematicae, Tome 122 (2011) pp. 49-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-4/