Progress on [5,2] and [5,4]
- x(x+1)(x+2)(x+3)(x+4) = x(X^2-1) = xX^2 - x
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.
xX^2 = Y^2 + x - 1
As x =approx. y^(4/5), x is not a square.
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