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Unformatted text preview: Math 465 Problem Set 1
1. Let a, b, c Z. Prove each of the following. (a) If ac|bc and c = 0, then a|b. (b) If a|b, then ac|bc. 2. Prove that if n is odd then 8 | n2 - 1. 3. Prove that 5 | n5 - n. 4. Prove that if 2p - 1 is prime then p is prime. Due Friday, January 25, 2008 5. Let a, m, n be positive integers with a > 1. Prove that am - 1 | an - 1 if and only if m | n. 1 ...
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