Arithmetic progressions of four squares over quadratic fields

Details Arithmetic progressions of four squares over quadratic fields Arithmetic progressions of four squares over quadratic fields

2009-03-23

arxiv.org/abs/0903.3856v1

Publicationes Mathematicae Debrecen 77/ 1-2 (2010), 125-138

Mathematics

Number Theory

Scientific paper

Let d be a squarefree integer. Does there exist four squares in arithmetic
progression over Q(sqrt{d})? We shall give a partial answer to this question,
depending on the value of d. In the affirmative case, we construct explicit
arithmetic progressions consisting of four squares over Q(sqrt{d}).

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