What is the difference between multiplicative group of integers modulo n and a Galois Field?
Is $\mathbb{Z}^*_p$ with p prime the same as $GF(p)$? Or is it the same as $\mathbb{Z}/n\mathbb{Z}$?
Sorry for the short and simple question, but this bit of notation is confusing me, so a clear different should help me alot!
Thanks!
If $p$ is prime then the ring $\mathbb Z/p\mathbb Z$ is in fact a field and is "the" field with $p$ elements (as there is only one up to isomorphism). Note however that for prime powers $q=p^n$ with $n>1$, the ring $\mathbb Z/q\mathbb Z$ is not a field, hence is different from the field $GF(q)$ (or $\mathbb F_q$, depending on author).