Project 6, 2015 | Research Experience for Teachers | Project 4, 2016 |
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Z*n |
Try to find a generator for a group. Select a number n from the drop box on the left. Select a number m from the horizontal list of numbers, all of which are prime relative to n. Click the Multiply button and watch boxes turn yellow. Each is m^{k} mod n for some k (given by the count textfield). A generator has been found if many clicks on Multiply turn all gray boxes to yellow. Use the reset button to try another generator. |
Observe:
If n is prime there is a number in Z*n, called a generator and denoted g, such that g^{i}, 1≤i<n, is unique, and an element of Z*n and g^{n-1} is 1. A generator for n = 19 is 10. |