Finding the order of a given element in a cyclic group

by user23473433819233d   Last Updated August 14, 2019 00:20 AM

Following on from my own example question in one of my previous posts I now want to better understand how to find the order of an element in a cyclic group G.

So in my previous example we had the group $G = \mathbb{Z}_{59}^{\times}$

I want to work out the order of 11 in group G. How would one compute and calculate this?

So far, I assume that you do 11^1 mod 59, 11^2 mod 59, 11^3 mod 59,..., 11^n mod 59 = 0?

Would be amazing to see how this would be computed and what other capabilities cyclic groups have

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