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Examining the series of real values of x for which f(x)=x^{2}+2cx+r is a perfect square, when m=c^{2}-r is the number we wish to factor, c is the Ceiling Root, and r is the difference between m and the Ceiling Square, is not evidently any better – and is in fact a slower and unenlightening process – than the current best factorization scheme I’ve formulated based on the Ceiling Square concept.

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