Abstract Algebra/Group Theory/Subgroup/Cyclic Subgroup/Euler's Totient Theorem

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Theorem[edit]

Let n be a positive integer. Let x be an integer relatively prime to n Let φ(n) = number of position integers less than and relatively prime to n

Proof[edit]

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 cylic 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.