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A quadratic identity

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  • Kermit Rose
    In another attempt to derive an unorthodox factoring algorithm, I came up with the following identity. If z = x y = r**2 + d, then x * ( x + y - 2 * r) = ( r
    Message 1 of 1 , Aug 1, 2008
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      In another attempt to derive an unorthodox factoring algorithm,

      I came up with the following identity.


      If z = x y = r**2 + d,

      then

      x * ( x + y - 2 * r) = ( r - x) **2 + d

      Proof

      x * (x + y - 2 * r) = x**2 + x y - 2 * x * r = x**2 + z - 2 * x * r
      = x**2 - 2 * x * r + z
      = x**2 - 2 * x * r + r**2 + d = ( r - x)**2 + d

      Kermit
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