(a) Let $F$ be a finite field of characteristic $p$. Show that $F$ is a finite Galois extension of the field $F_{p}$ of $p$ elements, and that the Galois group of $F$ over $F_{p}$ is cyclic.

(b) Find the Galois groups of the following polynomials:

(i) $t^{4}+1$ over $F_{3}$.

(ii) $t^{3}-t-2$ over $F_{5}$.

(iii) $t^{4}-1$ over $F_{7}$.