a) Make a power table for numbers mod 11. Indicate how the table shows Fermat's theorem, label the primitive roots mod 11. Explain how you can tell they are primitive roots. Label the rows that make good power ciphers and explain

b) using a computer, show that 7 is a primitive root mod 8745437489. Find a number alpha mod 8745437489 that is not a primitive root

c) Given that alpha is a primitive root mod p. Prove prove alpha^x is congruent to alpha^y mod p if and only if x is congruent to y mod p-1