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.
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