is a field of order 9. How do I find a generator for the cyclic multiplicative group of nonzero elements?
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Originally Posted by dori1123 is a field of order 9. How do I find a generator for the cyclic multiplicative group of nonzero elements? Let . All elements in this field are where . Therefore, the elements are: , , , , , , , , . You also know that so . From this list find an element so that . And that would be your generator.
Why are you letting , not .
Originally Posted by dori1123 Why are you letting , not . First because makes no sense since needs to be an element of and consists of cosets of . Second, is a basis for this field over . Therefore, everything has the form .
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