Quote from: bkelly13 on Today at 04:25:24 AM

Edit: shortly after posting, while doing something else, this thought occurred to me: Division is prohibited because it can, and more often than not, result in non-integer results.
Hmmm, but maybe that can be mitigated with some rules about those non-integral results.

There is no concept of "non-integer" in modular arithmetic. Actually, you shouldn't even think at integers, you can think as modular arithmetic as a set of ordered emoji (or fruits) as its elements. Division is not prohibited - it's simply non-existent, what you have is multiplication only. If the intent is to find some element by which you multiply to end up at the neutral element, this is what you would call "division". You can only use the tools offered by the structure.

Why not start off with the basic definitions of a Group, Field, prime field, before diving deep into elliptic curves (which are cyclic additive Groups) defined over some prime +* Field? Else you may get dizzy.