Prove the following:
1.Φ(n^k)= n^(k-1)•Φ(n)
2.Φ(Φ(p^n))=p^(n-2)•Φ((p-1)^2)
If I'm not mistaken, all you have to do is:
We know that:
So, with a little manipulation, we get:
And this turns out to be:
For the second one, note that:
Now, if we call the above answer m, we can see that p|m and we get:
But I'm not sure this is right, since you put ... So, hopefully this just gets you thinking.