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Math Help - proof help

  1. #1
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    proof help

    a and b are consecutive odd numbers, where a > b.
    Prove that a3 - b3 is 2 more than a multiple of 24.
    Fill in the gaps in the following proof.

    a is odd, so a = 2n+1 for some integer n.

    Then in terms of n, b =..............

    so a3 - b3 = (2n + 1)3 - ...............
    Expanding the brackets and simplifying,

    a3 - b3 = ............+ 2which is 2 more than a multiple of 24, as required.



    is b = 2n +1 <a ?

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  2. #2
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    Re: proof help

    a = 2n+1

    b = 2n+3
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  3. #3
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    Re: proof help

    Quote Originally Posted by skeeter View Post
    a = 2n+1

    b = 2n+3

    Thank you, but 'b' is less than 'a', so I dont understand how it can be 2n+3?, that would mean b is always going to be a bigger odd number than 'a'?
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  4. #4
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    Re: proof help

    my mistake ... so b = 2n-1
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