Primitive Roots in Polynomial Space
Contents
This question sucks.
1) Isolate the highest power of the polynomial modulo
2) If possible, apply the modulo to turn any negative terms into their equivalent positive term
3) Let $x = \alpha$
4) Express the powers of alpha in terms of the polynomial modulo
5) If you get a remainder of $1$ for a power that is not $n^p - 1$, try a different alpha substitution ($\alpha+1$ ?!?!)
Exponential Arithmetic
- $x^a * x^b = x^{a+b}$
- $(x^a)^b = x^ab$
- $x^{-a} = x^{highestpower - a}
Can express large powers as combinations of smaller powers
- A field has dimension $n$
- A field has $n^p$ vectors