Chapter 7 Exercise 1 |
This software determines when Z_{n} is the only group of order n in the case that n=pq where p and q are primes and p < q. Run the software for n = 3*5, 3*7, 3*11, 3*13, 3*17, 3*31, 5*7, 5*11, 5*13, 5*17, 5*31, 7*11, 7*13, 7*17, 7*19, and 7*43.
Conjecture a necessary and sufficient condition about p and q for Z_{pq} to be the only group of order
pq, where p and q are distinct primes. |