Consider the integral domain $\displaystyle Z(\sqrt10)=${$\displaystyle a+b\sqrt10|a,b \in Z$}

(a) Using the fact that the norm $\displaystyle N(a+b\sqrt10)=a^2 - 10b^2$ is multaplicative, describle the units of $\displaystyle Z(\sqrt10)$.

(b) Show that all four numbers: $\displaystyle 2,3,4+\sqrt10, 4-\sqrt10$ are irreducible. Are any of these numbers prime?

(c) Deduce that Z(\sqrt10) is not unique factorization domain.

My lecturer go though this topic too fast, so I have difficulty on above question. Please help me.