#### CSCI 3104 - Algorithms - Fall 2008

### Problem Set #2

#### Due: 3pm, Sep 22nd, 2008

1. Text problem 1.4.
2. Text problem 1.10.

3. Text problem 1.12.

4. Text problem 1.13.

5. Text problem 1.18.

6. Text problem 1.19. (Hint: use proof by induction)

7. Text problem 1.20.

8. Text problem 1.22.

9. What is the smallest 59-pseudoprime?

10. Text problem 1.27.

11. Text problem 1.42.

12. **(Extra Credit)** *Don't do this one until you've worked on
all others first! This is worth only a few points and is MUCH harder
than the other problems.*
Define f(0)=1 and f(x) = 7^{f(x-1)}. Find the last 10 decimal
digits of f(10). You'll probably want to use Python;
make sure you explain the technique you used!