Mapping generator to generator in cyclic groups.

jmjlt88
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Attached is my attempt at a proof. Please critque! :shy: Thank you!
 

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Note: Equation (1) in my proof is something that I proved in a prior exercise.

I did it by Mathematical Induction. I don't have it typed nicely, but I am pretty confident it worked.
 
Looks good! I don't see any issues.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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