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Math Help - even proof

  1. #1
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    even proof

    Hi, I need help on this problem:

    Let n \in \mathbb{Z} . Prove that  (n+1)^2 -1 is even if and only if  n is even.

    I wonder if you can use a proof by contrapositive to prove this.
    Any help will be appreciated. Thank you!
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  2. #2
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    Quote Originally Posted by MagicS06 View Post
    Hi, I need help on this problem:

    Let n \in \mathbb{Z} . Prove that  (n+1)^2 -1 is even if and only if  n is even.

    I wonder if you can use a proof by contrapositive to prove this.
    Any help will be appreciated. Thank you!
    If you can use the fact that any odd integer squared is odd then this seems straightforward. Assume n is odd and then proof by contradiction follows. Proving other way is easier. Use fact that any even integer squared is even and the result is trivially even.
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