Number Theory, with a proof discussed in class (not homework)

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Prove that ordda | ordma, when d|m.

Some conditions are 1 ≤ d, 1 ≤ m, and gcd(a,d)=1.

What I have so far:

let x=ordma, which gives us ax\equiv 1 (mod m) \Rightarrow ax=mk+1 for some k\inZ

Let m=m'd. Then ax=mk+1=d(m'k)+1
 
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Could someone give me a hint?
 
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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