411 REFERENCE · Wikibooks
Abstract Algebra/Group Theory/Subgroup/Cyclic Subgroup/Euler's Totient Theorem
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Theorem
Let n be a positive integer.
Let x be an integer relatively prime to n
Let φ(n) = number of positive integers less than and relatively prime to n
Proof
with multiplication mod n is a Group of positive integers less than and relatively prime to integer n.
φ(n) = o()
Let X be the cyclic subgroup of generated by x mod n.
As X is subgroup of
0. o(X) divides o()
1. o() / o(X) is an integer
2.