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hw4 - are co-prime(b Let a b d be integers such that 0 6 =...

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ECE 103 Discrete Math for Engineers University of Waterloo Spring 2010 Instructors: Koray Karabina, Ashwin Nayak Homework 4, due June 7, 2010 Note: All questions carry 5 marks. Question 1. Calculate gcd( - 1137 , - 419) using the Euclidean algorithm. Show all your calculations. Question 2. Find gcd(19201 , 3587) and integers x, y such that 19201 x + 3587 y = gcd(19201 , 3587). Show all your calculations. Question 3. (a) Prove that for any integer n , we have gcd( n, n +1) = 1 (i.e., any two consecutive integers
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Unformatted text preview: are co-prime ). (b) Let a, b, d be integers such that 0 6 = d = gcd( a, b ). Show that gcd( a/d, b/d ) = 1. Question 4. Let a, b, c be integers. Are the following statements true or false? Explain. (a) gcd( ab, c ) = gcd( a, c ) × gcd( b, c ). (b) If c is prime, and c | ( ab ), then c | a or c | b . Question 5. Find all the prime numbers between 160 and 170, prove that these are prime. 1...
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