Resumen de Arithmetic progressions of four squares over quadratic fields

Enrique González Jiménez, Jörn Steuding

• Let d be a squarefree integer. Does there exist four squares in arithmetic pro- gression over Q( p d )? We shall give a partial answer to this question, depending on the value of d. In the a±rmative case, we construct explicit arithmetic progressions consisting of four squares over Q( p d ).