Three cubes in arithmetic progression over quadratic fields
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چکیده
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Three cubes in arithmetic progression over quadratic fields
We study the problem of the existence of arithmetic progressions of three cubes over quadratic number fields Q( √ D), where D is a squarefree integer. For this purpose, we give a characterization in terms of Q( √ D)-rational points on the elliptic curve E : y = x − 27. We compute the torsion subgroup of the Mordell–Weil group of this elliptic curve over Q( √ D) and we give an explicit answer, i...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2010
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-010-0166-5