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Question: problem 1 10 points let p be a prime number...

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Problem 1 (10 POINTS): Let p be a prime number and k1 a positive integer. Denote m 2p and let a be a positive integer, relatively prime to m. (a) Suppose p > 2. Show that a-1-a (mod m) (E士1 (mod m) (b) Suppose p-2. Show that a-1-a (mod m) (E or a-2k t l (mod m). (c) Assume now that n is any positive integer. How many solutions does the modular equation a1- a (mod n) have? Hint: Use the Chinese Remainder Theorem!

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