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.