We have seen for all integers 
So if p is a prime number, we have seen
that each of these fixed points of f_{n}^{p} belongs to a

We have seen that f_{n} has n fixed points. 
Consequently, 
Each 
That is, for all prime numbers p and for all integers 
p divides n^{p}  n. 
This is Fermat's Little Theorem. 
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