hw2 - a | c , and b | c , then ab | c . 4. Show that if...

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Math 465 Problem Set 2 Due Friday, February 1, 2008 1. If ( a, c ) = 1 and ( b, c ) = 1, then ( ab, c ) = 1. 2. Show that if ( a, b ) = 1, then ( a - b, a + b ) = 1 or 2. When is the value 2? 3. Let a, b, c Z with a 6 = 0 and b 6 = 0. Show that if ( a, b ) = 1,
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Unformatted text preview: a | c , and b | c , then ab | c . 4. Show that if ad-bc = 1, then ( a + b, c + d ) = 1. 5. Find ( a, b ) and express the gcd in the form ax + by . (a) a = 361 , b = 1178 (b) a = 525 , b = 231 1...
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