As we have seen in Section 2.1, an element a of Z/nZ is invertible if and only if gcd(a,n)=1.
Definition
For n 
N, we denote by 
(n) the number of elements in {1,
..., n} that are relatively prime with n. The function : N -> N is called the Euler
indicator.
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Thus
(n) is the number of
invertible elements in Z/nZ.
It can be determined by means of the following
recursion.
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Theorem
The Euler indicator satisfies the following rules.
- (1) = 1;
- (n) = n
-
d|n, n>d>0
(d).
For prime powers this gives a
closed formula for the Euler indicator.