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Progress on [5,2] and [5,4]

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  • Jon Perry
    x(x+1)(x+2)(x+3)(x+4) = x(X^2-1) = xX^2 - x Consider [5,2] xX^2 = y^2 + y + x if (y^2+x) is a square, then x is not a square. if (y^2+y+x) is a square, then x
    Message 1 of 1 , Sep 27, 2001
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      x(x+1)(x+2)(x+3)(x+4) = x(X^2-1) = xX^2 - x

      Consider [5,2]

      xX^2 = y^2 + y + x

      if (y^2+x) is a square, then x is not a square.

      if (y^2+y+x) is a square, then x is a square

      xX^2 = (y+1)^2 + x - y + 1

      As x =approx. y^(2/5), the RHS is not a square, therefore x is not a square.

      Consider [5,4]

      xX^2 = Y^2 + x - 1

      As x =approx. y^(4/5), x is not a square.

      Jon Perry
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