Assignments: 
Nr 
Exercises 
Due date 
1 
1.3, 1.12, 1.20 
Jan. 20 
2 
 What happens to Theorem 21 if d=1?
 2.8, 2.16, 2.21, 2.23
 Correlate 2.11 with 1.3

Feb. 3 
3 
 3.35, 3.42
 This question concerns Theorem 3.43. First, let S be a finite set of primes. We say that a rational number is an Sinteger (element of Z_{S})
if its denominator consists entirely of prime factors from S. Can we modify the prove the statement of Theorem 3.43 for Sintegers as well?
 This question concerns the proof of Theorem 3.35. Consider the equation X^43Y^4=B. If we adjoin sqrt(3), we can write X^43Y^4=(X^2sqrt(3)Y^2)(X^2+sqrt(3)Y^2), so perhaps we can avoid using Roth's theorem and use the same argument that applies if the form factors over Z already. What goes wrong?

Mar. 1 
4 
4.1, 4.6 
March 31 
5 
6.1, 6.8, 6.10 
April 14 
