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 $\phi(n)$?