b. Suppose a is some primitive root of 19 (it must exist for any prime!). - What is the order of a², a³, aª, and a5 (mod

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B Suppose A Is Some Primitive Root Of 19 It Must Exist For Any Prime What Is The Order Of A A Aa And A5 Mod 1 (94.45 KiB) Viewed 34 times

b. Suppose a is some primitive root of 19 (it must exist for any prime!). - What is the order of a², a³, aª, and a5 (mod 19)? - What elements ak (mod 19) k = 2,... 18 will also be primitive roots of 19? (Formulate as an easy-to-use rule and justify.) - Are these all primitive roots? (Compare to the results from Thm. 3.28). c. We are given that 3 is a primitive root of 19. Using (b), find all numbers from 2 to 18 which are the primitive roots of 19. Explain.