The minuend of any such square-difference expression of m will then be greater than m’s ceiling square. Define the ascent of such a factorization or corresponding square-difference expression as the difference between the square root of the minuend in that expression and the ceiling root of m.
The ascent of the trivial factorization 1*m will always be (m+1)/2-s, where s is the ceiling square of m.
For factorization m=ab, the ascent is (a+b)/2 – s.
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