Found some interesting references.
[thread at another forum] Iteration of Euler's phi function
[pdf] On the Sum of Iterations of the Euler Function
Possibly something could be done with the inequalities in this Wikipedia article.
This thread got me thinking...
Define and so on...
Now Define to be the smallest integer such that .
I've found some bounds of : it's easy to see and a delicate strong induction shows .
My question is, what the formula for , or at least what are some tighter bounds?
-Thanks!
Found some interesting references.
[thread at another forum] Iteration of Euler's phi function
[pdf] On the Sum of Iterations of the Euler Function
Possibly something could be done with the inequalities in this Wikipedia article.
A lower bound, ... I'll have to be thinking about it, it's quite interesting. And any bounds found will be highly valuable to my final project (I'm going to use the result proved in my thread into a bigger algorithm).
First I have to see if there are any lower bounds existing yet. It could be a starting point.
I'm building up an improvement to Pollard's p-1 integer factorization algorithm. The project is going to use the general theorem proved in my thread, the bounds on the iteration of the totient function, and a variant of a quick modular exponentiation method. It should work.