everyone. I am having difficulties with this question.
Let $K = \mathbb{Q}(\sqrt{d})$ be a real quadratic field , and $ \mathcal{O}_K$ be the ring of integers of $K$. By making use of $u$, a fundamental unit (coming from a solution of the Pell equation), show that there is no such thing as the smallest possible positive integer in $\mathcal{O}_K$ (in the sense of the usual order of the real numbers).
Thank you in advance.