Ciro Santilli $$ Sponsor Ciro $$ 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件 邓家贵、低端人口、西藏骚乱
A convenient notation for the elements of of prime order is to use integers, e.g. for we could write:
which makes it clear what is the additive inverse of each element, although sometimes a notation starting from 0 is also used:
For fields of prime order, regular modular arithmetic works as the field operation.
For non-prime order, we see that modular arithmetic does not work because the divisors have no inverse. E.g. at order 6, 2 and 3 have no inverse, e.g. for 2:
we see that things wrap around perfecly, and 1 is never reached.
For non-prime prime power orders however, we can find a way, see finite field of non-prime order.
Video 3. Finite fields made easy by Randell Heyman (2015) Source. Good introduction with examples

Ancestors