After some study, the author has discovered that the ascent – the difference between the ceiling root of m and the value of s so that one can form a non-trivial s^{2}-t^{2} expression of m – corresponds to the value of n one finds when expressing prime factors p and q in terms of the ceiling square of m. If p < q and CR is the ceiling root of m, one can determine c_{1} and c_{2} so that p = CR – c_{1} and q = CR + c_{2}. Setting n = c_{2}-c_{1} makes n equal to twice the ascent of the factorization. The ascent is through this a familiar concept explored earlier in this study, and its mysteries are arguably no closer to revealing themselves.

It’s like in “Beetlejuice” when the Maitlands end up in a room that’s crazier even than the last several in which they have wandered, and Adam looks around, then slowly and softly says, “Barbara, … we’re home.”

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