Is the following statement true ?
If so, please explain why.
If K is an algebraically closed field, then K is an infinite set.
Every finite field has order for some n. The underlying multiplicative group is always cyclic (of order ). Thus, for all .
Therefore, if , the equation will not have a root in .
If then this trick doesn't work...however, if is your finite field, then the polynomial has no roots in (this works for all p).