It is given that 3023 is prime, and 3023 = 2(1511) +1 where 1511 is also prime. (a) How many primitive roots does 3023 have? (b) Show that 5 is a primitive root of 3023. (C) It is given that 5164 = 42 (mod 3023). What is the order of 42 modulo 3023? What is the order of 210 modulo 3023 (210 = 42 - 5)? (d) How many solutions does a164 = 42 (mod 3023) have?

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