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Avalg homework B fall 2007 This homework is due 14/11. It should be done individually and handed in at the beginning of the homework session. You should be prepared to present your homework orally in class. This is part of the examination and you have to attend the homework session to get credit for your homework. Solutions handed in late are not accepted and will not be graded. 1. Compute the order of 3 modulo 13. (5p) 2. Let p be a prime. Prove that Z/pZ is a field. (5p) 3. For what values of n is phi(n) odd? (5p) 4. Show that if p is a positive integer such that both p and p2 + 2 are prime, then p = 3. (5p) 5. Let a and b be positive integers and p prime. Prove that gcd(pa - 1, pb - 1) = pgcd(a, b) - 1. (5p) Stefan Nilsson 2007-10-31 |