In section 1.6, we learned about orders of congruence classes, Fermat's little theory, Euler's theorem, and the totient function as they apply to RSA encryption.
1. What is $[2]_{8}^{10}$?

2. What is $[3]_{8}^{10}$?

3. What is the order of $[3]_{8}$?

4. What is the order of $[2]_{11}$?

5. What is the order of $[3]_{11}$?

6. What is the order of $[7]_{14}$?

7. If a = and n = , what is the order of $[a]_n$?

8. What is $\phi(2^{3})$?

9. What is $\phi(3^{2})$?

10. What is $\phi(7^{2})$?

11. What is $\phi(2^{6})$?

12. What is $\phi(5^{3})$?

13. What is $\phi(3 \times 5 )$?

14. What is $\phi(7 \times 11 )$?

15. What is $\phi(17 \times 3 )$?

16. What is $\phi(5 \times 29 )$?

17. What is $\phi( 500 )$?

18. What is $\phi( 120 )$?

19. What is $\phi( 100 )$?

20. Let's calculate a totient. If n = , what is $\phi(n)$?