Question 8
a) Let $m, n, p \in \mathbb{N}$, with $m \gt n$, such that $\sqrt{m} - \sqrt{n} = p$. Prove that $m$ and $n$ are both squares.
b) Find, with proof, all numbers $\overline{abcd}$ such that $\sqrt{\overline{abcd}} - \sqrt{\overline{acd}} = \overline{bb}$.
b) Find, with proof, all numbers $\overline{abcd}$ such that $\sqrt{\overline{abcd}} - \sqrt{\overline{acd}} = \overline{bb}$.