189-235A: Algebra 1

Assignment 3

Weeks of Sept 21-25

1. Exercise (1) of page 50 of the notes.

2. Exercise (2) of page 50 of the notes.

3. Exercise (3) of page 50 of the notes.

4. exercise (4) on page 50 of the notes.

5. Exercise (7) on page 50 of the notes.

6. Exercise (13) on page 50 of the notes.

7. Show that any prime divisor of $2^{2^n}+1$ is of the form $1+2^{n+1}$.

8. What day of the week will it be on September 21, 2027 and on September 21, 2028, (knowing that September 21, 2026 is a Monday, and that neither 2027 or 2028 are leap years)? You should explain how to find the answer using only pen and paper, no google search or (perish the thought) appeal to AI.