{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 210hw6 - can’t order 5 Let A = n m n ∈ Q ± ± ± 7-n...

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: can’t order? 5. Let A = n m n ∈ Q ± ± ± 7-n o . (i) List three elements of A . (ii) List three rational numbers that don’t 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...
View Full Document

{[ snackBarMessage ]}