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Math Help - need integer square root

  1. #1
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    Sep 2011
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    need integer square root

    In another thread I have ended up with this equation

    y=\dfrac{(3v_1+u_1)\pm\sqrt{u_1^2+6u_1v_1+v_1^2}}{  2}

    I need y to be an integer <> 0, so the first requirement is that

    u_1^2+6u_1v_1+v_1^2 be a perfect square

    If I go at it like this

    x^2=u^2+6uv+v^2


    x^2=(u+v)^2+4uv


    x^2-(u+v)^2=4uv


    (x+(u+v) )(x-(u+v) )=4uv


    let\ \ \ \ \ x+(u+v)=r


    and\ \ \ \ x-(u+v)=s


    x=(r+s)/2


    u+v=(r-s)/2


    uv=rs/4

    But I have no individual values of u and v now so cannot calculate

    3v_1+u_1

    Anyone have any other ideas how I can ensure u_1^2+6u_1v_1+v_1^2 is a perfect square?
    Last edited by moriman; September 29th 2011 at 11:39 AM. Reason: submitted early by mistake
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