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Math Help - Indirect Proof question

  1. #1
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    Indirect Proof question

    Using and indirect proof prove that if n is an integer and 5n^2+ 19 is even, then n is
    odd.
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  2. #2
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    Re: Indirect Proof question

    Quote Originally Posted by Benja303 View Post
    Using and indirect proof prove that if n is an integer and 5n^2+ 19 is even, then n is
    odd.
    Suppose n were even.

    $5 n^2 + 19=5(2k)^2+19=20k^2+19$

    $20 k^2 + 19$ is clearly odd for any k and thus by contradiction n must be odd.
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  3. #3
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    Re: Indirect Proof question

    A little more detail: Suppose n were even. Then n= 2k for some integer k. 5n^2+ 19= 5(2k)^2+ 19= 5(4k^2)+ 19= 20k^2+ 19= 20k^2+ 18+ 1= 2(10k^2+ 9)+ 1. Since 5n^2+ 19 is equal to 2 times an integer plus one, it is odd, not even, a contradiction.
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