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