210hw6 - cant order? 5. Let A = n m n Q 7-n o . (i) List...

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Math 210 Homework 6 Due Monday March 21st 1. Let a and b be integers. Prove that 3 a + b is divisible by 7 if and only if a + 5 b is divisible by 7. 2. True or false? In each case, if true, give a general proof. If false, give an explicit counterexample. (All variables represent integers.) (i) If a | b and a | c , then a | bc . (ii) If a | c and b | c , then ab | c . (iii) If a | b and c | d , then ac | bd . 3. Suppose a and b are relatively prime integers and c is an integer such that a | c and b | c . Prove that ab | c . 4. It’s the 1980s, and Chicken McNuggets only come in packets of 6, 9, and 20. By combining 6, 9, and 20, other numbers can be formed, such as 15 (6 + 9) and 46 (20 + 20 + 6). What’s the largest number of McNuggets you
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Unformatted text preview: cant order? 5. Let A = n m n Q 7-n o . (i) List three elements of A . (ii) List three rational numbers that dont belong to A . (ii) Prove that A is closed under addition and closed under multiplication. 6. True or false? Explain. (i) n N , prime p such that p | n . (ii) prime p such that n N , p | n . 7. Determine whether the function f : N N N is one-to-one. (i) f ( n,m ) = 2 m 6 n (ii) f ( n,m ) = 36 m 6 n 1 2...
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This note was uploaded on 12/07/2011 for the course MATH 210 taught by Professor Staff during the Spring '08 term at University of Delaware.

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210hw6 - cant order? 5. Let A = n m n Q 7-n o . (i) List...

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