Solutions to xyz = 1 and x+y+z = k in algebraic integers of small degree, I

H. G. Grundman; L. L. Hall-Seelig

Acta Arithmetica, Tome 166 (2014), p. 381-392 / Harvested from The Polish Digital Mathematics Library

Résumé

Let k ∈ ℤ be such that $|_{k} (ℚ) | = 3$ , where $_{k} : y ² = 1 - 2 k x + k ² x ² - 4 x ³$ . We determine all solutions to xyz = 1 and x + y + z = k in integers of number fields of degree at most four over ℚ.

Publié le : 2014-01-01

Zbl 06270724

EUDML-ID : urn:eudml:doc:279779

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     title = {Solutions to xyz = 1 and x+y+z = k in algebraic integers of small degree, I},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {381-392},
     zbl = {06270724},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-4-5}
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H. G. Grundman; L. L. Hall-Seelig. Solutions to xyz = 1 and x+y+z = k in algebraic integers of small degree, I. Acta Arithmetica, Tome 166 (2014) pp. 381-392. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-4-5/