Show that \(\mathcal{O}_{K}/\mathfrak{p}\simeq\mathbb{F}_{q}\) where \(q=[\mathcal{O}_{K}:\mathfrak{p}]\) is either \(p\) or \(p^{2}\), with \(\mathfrak{p}=(p,\alpha)\). Give an explicit criterion in terms of \(p\) and \(d\) for when the two cases occur.