Re: Algebra

["Perry E. Metzger" <perry@imsi.com>]

Tom Jones says:
> Dear Eric and Cypherpunks,
> 
> So, how is division defined in Fp?

Being an old fogey, I still refer to the field formed by the integers
modulo a prime by a gothic capital Z sub p.

In Z_p, you define division as the inverse of multiplcation, just as
in real life. One easy way to do this is to note that every number in
a field like this has a multiplicative inverse. Multiplying by the
multiplicative inverse of a number is the same as dividing by the
number. 

For the hell of it, make yourself a multiplication table for Z_5. Its
a quick exercise. Note that every number in Z_5 other than zero
possesses a multiplicative inverse -- that is, a number that it can be
multiplied against to yield 1. Step back and then observe,
experimentally, that for any three positive numbers in Z_5 A, B and C
such that A*B=C, that C*(B^-1)=A. One can, of course, prove that this
is the case rigorously...

Perry