This reminds me of Ken Thompson’s speech on trusting trust. The recursive/meta nature of it all has helped me explain to those unfamiliar that this is such a waste of time. Education is where it’s at, but I’m preaching to the choir here on HN.
I'm trying to understand 5). If you're claiming that both (A) y > x, and (B) x^y > y^x hold, then x^y > y^x ("will always be larger") holds. You're satisfying your claim by assumption. Nothing new is deduced.
However, if only A) needs to be satisfied: y = 3, x = 2 is a counterexample, as x^y = 2^3 = 8 < 9 = 3^2 = y^x.
edit: looks like someone had the same thought as me as I was typing my reply!
Unless I'm missing something, the definition of H_division is misleading. The co-domain (image) set is really {0, ..., M - 1}, which _is_ surely a subset of [0, M), although definitely very different in size. Usually it's written as Z/qZ where q = M.
Neat article otherwise. It reminded me of mappings to real numbers which I always found interesting during my undergrad.
I will agree that this is generally a good way to go, although in my experience there have been quite a few individuals that I end up no longer admiring.