Now we will consider equations of the form x m = a, in a field K (or occasionally in a ring); the case a=1 has been discussed in § X. As the case a=0 is trivial, we assume a≠0. If then, in the field K, x is a solution of xm=a, an element x’ of K is also a solution if and only if (x’/x) m =1. Therefore, if xm=a has a solution in K, it has as many solutions as K contains mth roots of unity, i.e. roots of X m -1.
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