Fuzzy groups and level subgroups

Let ? be an algebraic integer in a quadratic number field whose minimum polynomial is x² + p₁ + p₀. Then all the elements of the ring $\text{|Z}$?] can be written uniquely in the base ? as Σ_k^m=0^akπ^k, where 0 ? a_k < |p₀|, if and only if p₀ ? 2 and ?1 ? p₁ ? p₀.