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Math Help - Perfect Square combinatorics proof

  1. #1
    Junior Member
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    Perfect Square combinatorics proof

    Hello again!

    My question reads:

    If n is a positive integer and n > 1, prove that C(n,2) + C(n-1,2) is a perfect square.

    Anyway, I went ahead and simplified the statement, which brought it to this:

    n^2 - 2n + 1

    In this form, it's fairly obvious that for any selected value of an integer n greater than one, it will be a perfect square.

    What I'm wondering is if there's a better way to conclude the proof, or if that answer seems suitable.

    Thank you for your time.
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  2. #2
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    Write this:

    since  {n^2} - 2n + 1 = (n-1)(n-1) = {(n-1)^2}

    any  n\in\\N : n>1 will be a perfect square.
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