Question 49
Let $(K, +, \cdot)$ be a finite field. Prove that:
a) if $K$ has $4k+1$ elements, then the polynomial $f = X^4 + 4$ has four roots in $K$;
b) the polynomial $g = X^8 - 16$ has at least a root in $K$.
a) if $K$ has $4k+1$ elements, then the polynomial $f = X^4 + 4$ has four roots in $K$;
b) the polynomial $g = X^8 - 16$ has at least a root in $K$.