ABSTRACT
Since the beginning of computer technology the field Z 2 has had important applications, with “1” denoting a closed circuit and “0” denoting an open circuit. Since computers use more than one circuit, a natural and important question is whether there are fields whose orders are higher powers of 2, or of other orders. So far we know Zp is a field for p prime, so, in particular, there are fields of order 2,3,5,7, and so forth. What about 4 and 6? More generally, we want to tackle the following two questions, given n in N :
(1) Is there a field of n elements? (2) Are there two nonisomorphic fields of n elements?
