Abstract
Let ϱ be an algebraic integer in a quadratic number field whose minimum polynomial is x 2 + p 1 + p 0. Then all the elements of the ring |Z [ϱ] can be written uniquely in the base ϱ as Σ k m =0 a kπ k , where 0 ⩽ a k < | p 0|, if and only if p 0 ⩾ 2 and −1 ⩽ p 1 ⩽ p 0.
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