Once had my own method for calculating the modular inverse gained a LOT more perspective on my situation. So yeah there's a recursive method for calculating the modular inverse which I discovered.
Meaning now there are three primary ways to figure out a modular inverse versus only two PRIMARY ways, before. Putting me in company with Euler and oddly enough, Euclid.
One of my best posts deriving: Meta and my modular inverse method
Where stepped through in more detail than had prior. Which was good! And gave an example calculating modular inverse of 35 mod 101, which is 26. So yeah, thankfully verified what I already had, and helped me understand better.
Where will edit to add realized the key expression is: F = r(r + 2my) mod N
And have F self-referencing itself with two added control variables n and d, where F0 is initial F value, and y0 is initial y. So yeah, while I derive to there from another key expression turns out the above is technically all I need.
So yeah I do yet another thing NOT intuitive in adding two variables for control purposes. Yet I did, and that's why I have the result. Often just wonder and wonder at simple answers, after. Will admit is a fun thing to find puzzling.
Also have talked SOME big picture things even more recently:
Thoughts on my modular inverse derivation and possible algorithm
Where realized how fast potentially it might be.
Have noted before that math and emotion do not mix well. And for me can end up on a roller coaster of emotions where thankfully have been through it before, with prior major discoveries.
Still this time...yeah, math and emotion do not mix well.
Is weird, to some extent will run away from results like this discovery. Then come back to it, eventually. Study a bit, run away again. And ponder. Run away again. Until finally is acceptance and am like, is cool.
Yeah, math and emotion do not mix well.
Can be overly dramatic I think. Where also should emphasize the wonder that is math as regardless of your feelings? You can check. And readily admit going over arguments over and over and over again. Where part of you is like, nothing is going to change here.
But also finding new ways to explain, or making sure to explain in EXTREME detail, to the point of using my own definition of mathematical proof...ok, I always do that one. As how else can I be sure?
Yeah at some point, will check to be sure began with a truth, then will check EACH step from there as to logic of it, until get to conclusion which I then know must be true, intellectually.
James Harris
