HW 9, due Wed Nov 16

• MNT 12.1
• MNT 12.2  You may compute the discriminant with respect to the basis $1, \sqrt{2}, (1+\sqrt{5})/2, (1+\sqrt{5})\sqrt{2}/2$.
• MNT 12.4.  In this problem “integer” means algebraic integer, the conjugate of $\alpha = a + b \sqrt{d}$ means  $\alpha' = a- b\sqrt{d}$.  Also, $|\alpha|$ is the absolute value of $\alpha$ (viewed as a complex number).  Hint: can you bound the number of quadratic monic polynomials with integer coefficients?
• MNT 12.6
• MNT 12.9.  You may work this for an irreducible cubic rather than a reducible cubic, if you prefer, using 12.1.4.