8. Let F = Q(\sqrt{D}) be a quadratic field with associated quadratic integer ring O and field norm N as in Section 7.1.
(a) Suppose D is -1, -2, -3, -7 or -11. Prove that O is a Euclidean Domain with respect to N. [Modify the proof for Z[i] (D = -1) in the text. For D = -3, -7, -11 prove that every element of F differs from an element in O by an element whose norm is at most (1 + |D|)$^2$/(16|D|), which is less than 1 for these values of D. Plotting the points of O in C may be helpful.]
