hw7 - ( a + 1) 2 and ( a + 1) 3 modulo p .) 4. Find a...

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Math 465 Problem Set 7 Due Friday, March 28, 2008 1. Find the order of 2 , 3 , and 5 modulo 23. 2. Prove that φ (2 n - 1) is a multiple of n for any n > 1. (Hint: The integer 2 has order n modulo 2 n - 1.) 3. Let a has order 3 modulo p . (a) Show that a 2 + a + 1 0 (mod p ). (b) Show that a + 1 must have order 6 modulo p . (Hint: Use part (a) to compute
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Unformatted text preview: ( a + 1) 2 and ( a + 1) 3 modulo p .) 4. Find a primitive root modulo 11. How many primitive roots does the prime 11 have? 5. Show that if a is a primitive root modulo p 2 , then it is a primitive root modulo p . 1...
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