| 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 S-integer (element of ZS)
if its denominator consists entirely of prime factors from S. Can we modify the prove the statement of Theorem 3.43 for S-integers as well?
- This question concerns the proof of Theorem 3.35. Consider the equation X^4-3Y^4=B. If we adjoin sqrt(3), we can write X^4-3Y^4=(X^2-sqrt(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 |
|