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Math Help - Prove this function equation

  1. #1
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    Prove this function equation

    This is how & works:
    &(19, 14) = (5, 0) and &(12, 15) = (0, 3)

    How do I show &^2 = &
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  2. #2
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    Quote Originally Posted by jzellt View Post
    This is how & works:
    &(19, 14) = (5, 0) and &(12, 15) = (0, 3)

    How do I show &^2 = &
    I'm going to guess that the general form of this is: &(a,b)=(a-b,0) (when a>b) and &(a,b)=(0,b-a) (when b>a). &^2 doesn't make sense to me since & is being defined as an operation on two numbers a,b and means nothing by itself thus can't be squared. Can you explain more please?
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  3. #3
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    Quote Originally Posted by Jameson View Post
    I'm going to guess that the general form of this is: &(a,b)=(a-b,0) (when a>b) and &(a,b)=(0,b-a) (when b>a). [snip]
    Nice guess!

    To show && = & I think you would want to show that &&(a,b) = &(&(a,b)) = &(a,b). Given the above good work in defining &(a,b), it is trivial to do this ....
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