What are all of the distinct generators of Z17 with respect to multiplication? What are all the distance generators of Z19 with respect to multiplication?
What are all of the distinct generators of Z17 with respect to multiplication? What are all the distance generators of Z19 with respect to multiplication?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
Problem 29EQ: Write out the addition and multiplication tables for 4.
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What are all of the distinct generators of Z17 with respect to multiplication?
What are all the distance generators of Z19 with respect to multiplication?
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We have to find the all distinct generators of with respect to multiplication.
Recall the corollary
The multiplication group of all nonzero elements of a finite field is cyclic.
Note that the unity of is .
If is a generator of the multiplicative group if and only, where goes over divisors of .
Compute in
Since,
Hence, is a generator of .
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