hw08 - class Definition Let n ∈ Z We say that n is a...

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Intro to Abstract Math Homework 8 Fall 2009 Due September 23 Exercise 25. Let a,b,c Z . Prove that if a | b and b | c then a | c . Exercise 26. Prove that for all n N , 5 n - 1 is divisible by 4. Exercise 27. Assume that n is an integer. Prove that for all n 2, n can be written as a product of primes (defined below). [ Hint: Modify the proof on prime numbers given in
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Unformatted text preview: class.] Definition: Let n ∈ Z . We say that n is a product of primes if there exist r ∈ N and prime numbers p 1 ,p 2 ,...,p r (not necessarily distinct) so that n = p 1 p 2 ··· p r . Notice that, since we can have r = 1, every prime number is a product of primes....
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