- MNT 12.1
- MNT 12.2 You may compute the discriminant with respect to the basis .
- MNT 12.4. In this problem “integer” means algebraic integer, the conjugate of means . Also, is the absolute value of (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.