Let , where m is a square-free integer. Let be an algebraic integer in K.

a) Show that the minimum polynomial of a is

Now, I have verified that

And I have to prove it is irreducible over K, should I use the norm, but the norm is not defined here yet, can I use N(ax+b) = a^2 + b^2?

I factored the polynomial into , will this help?

b) Show that are integers.