a4 - ab,c ) = gcd( b,c ) if gcd( a,c ) = 1. Is it true in...

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Assignment 4 – Questions 1. Suppose that m,n P . Prove that if m 2 6 | n 2 , then m 6 | n . (Hint: consider the contrapositive.) 2. Find integers s and t such that ( - 5083) s + (1656) t = gcd( - 5083 , 1656) . 3. Prove that for all integers a,b,c with c > 0, we have gcd( ac,bc ) = c gcd( a,b ). 4. Prove that gcd(
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Unformatted text preview: ab,c ) = gcd( b,c ) if gcd( a,c ) = 1. Is it true in general that gcd( ab,c ) = gcd( a,c ) gcd( b,c ) ? Justify your answer. 5. Prove that for all integers a,b , we have gcd( a,b ) = gcd(2 a + b, 3 a + 2 b ). 1...
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