Assignment 4 - m 6 | n , then m 2 6 | n 3 , is false....

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MATH 135, Fall 2010 Assignment #4 Due at 4:00pm on Tuesday, October 12 For the online MapleTA assignment, please go to http://mapleta.uwaterloo.ca/ . Problem 1 . Let a,b,c Z . Prove that if ac | bc and c 6 = 0, then a | b . Problem 2 . (a) Let m,n P . Prove that if m 2 6 | n 3 , then m 6 | n . (Hint: Use the contrapositive law.) (b) Show that the converse of the above statement is false; i.e., the statement that if
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Unformatted text preview: m 6 | n , then m 2 6 | n 3 , is false. (Hint: Use a counterexample.) Problem 3 . Let a,b,n Z . Prove that if n > 0, then gcd( an,bn ) = n gcd( a,b ). Problem 4 . Let a,b Z . Prove that gcd( a,b ) = gcd(2 a-3 b,a-2 b ). Problem 5 . Let a,b,c Z . Prove that gcd( ab,c ) = 1 if and only if gcd( a,c ) = gcd( b,c ) = 1. 1...
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This note was uploaded on 12/18/2010 for the course ECONOMICS 120 taught by Professor Mesta during the Spring '10 term at Wilfred Laurier University .

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