>>5345

I'm not really sure what the scissors context is, but the approximations you're seeing are actually exact equalities, give or take your calculator's precision:

If C = p * P, then √C = √p * √P,

so P / √C = (P / √P) / √p = √P / √p

and √C / p = √P * (√p / p) = √P / √p, the same.

>>5450

Generally in talking about algorithm complexity, constant factors are ignored, so log2, ln, log10, etc. are all considered essentially the same.

That said, an even-odd decision tree or a normal binary search (like the square root code) would end up as log of the value c, since you get about one bit of the answer per iteration. Something that scales as the log of the number of bits of c is like log(log c), which is… shockingly efficient.

>>5517

Those non-solution x+n values are (a-1)/2 and (b-1)/2, so if you subtract them, you just get x+n = (b-a)/2.

>>5519

Only if you already know a and b, heh heh.