**Homework for Mathematics of Information Security **

M360: Fall 2004

** HW 6: due Friday 10/1**

READ: Sections 3.4, 3.6 (again), 2.12 (just for the main idea).

BOOK PROBLEMS: 3.11 #6, #9.

OTHER PROBLEMS:

A. Find phi(97) and phi(8800).

B. If m > 2, explain why phi(m) is always even.

C. Find all m so that phi(n)=n/2.

D. If p and q are distinct primes, find a formula for phi(pq).

E. Suppose m is a number so that phi(m)=1000.

Find a number b between 1 and 2000 so that b = 7^(3003) mod m.

F. Find x so that x=3 mod 7 and x=5 mod 9.

G. Explain why there is no solution to x=2 mod 6 and x=3 mod 4.

Bonus:

* Describe all values of m for which 4 does not divide phi(m).