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In this problem you will complete the details of an indirect proof Fill in the...

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Basic Math

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In this problem you will complete the details of an indirect proof Fill in the blanks below Each blank should be filled with a polynomial in the variable k Prove Let n be an integer If n 17 is even then n is odd Proof Suppose that n 17 is even Assume for the sake of contradiction that n is even By definition n 2k for some integer k So n 17 2k 17 2m 1 where m Since Z is closed under addition and multiplication m e Z Since n 17 2m 1 this means that n 17 is odd However this contradicts the fact that n 17 is even Therefore n must be odd

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