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Unformatted text preview: MATH 135 Fall 2008 Assignment #6 Due: Wednesday 29 October 2008, 8:20 a.m. HandIn Problems 1. In parts (a) to (d), state the answer. No justification is necessary. In parts (e) to (h), explain how you got your answer. (a) Is 14 22 (mod 18)? (b) Is 2473  26 (mod 17)? (c) Is 8 16 4 (mod 12)? (d) For how many n P with 1 n 2008 is n 0 (mod 4)? (e) What is the remainder when 8 243 is divided by 3? (f) Is 8 24 + 13 12 divisible by 7? (g) Determine the remainder when 3 47 5 74 + ( 9) 10 is divided by 13. (h) For how many m P with m > 1 is 14  58 (mod m )? 2. Suppose that a,b Z and m P , with a b (mod m ). Prove by induction that a n b n (mod m ) for every n P . 3. Suppose that a,b Z and m,n P . Prove that an bn (mod mn ) if and only if a b (mod m ). 4. Suppose that p is a prime number with p > 3. (a) By consider the possible remainders when p is divided by 4, prove that p 1 or 3 (mod 4)....
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 Fall '08
 ANDREWCHILDS
 Math, Algebra

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