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Math Help - help on a concept

  1. #1
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    help on a concept

    every odd integer can be written as 4k+1 which I understand because you can break it down to 2(2k) + 1. But here is the part I don't get, every odd integer can also be written as 4k + 3 for an integer k.

    It says this is true in the back of my book but I don't understand why?
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  2. #2
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    Quote Originally Posted by FamilyGuy34 View Post
    every odd integer can be written as 4k+1 which I understand because you can break it down to 2(2k) + 1. But here is the part I don't get, every odd integer can also be written as 4k + 3 for an integer k.

    It says this is true in the back of my book but I don't understand why?
    Both of the above statements are false.

    every odd integer can be written as 4k+1
    What about 3 4k+1=3 \implies k=\frac{1}{2} and one half is not an integer.

    every odd integer can also be written as 4k + 3 for an integer k.
    This is also false. 5 is an odd integer but

    4k+3=5 \implies k =\frac{1}{2}
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