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hwangs12
hwangs12

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Totient Function Of A Prime

Statement

Totient function of a prime number p is p-1.

Proof

Suppose Φ(p)<p−1 \Phi (p) < p-1 . This means that there is a positive integer less than p which share a prime factor other than 1. However, prime numbers are divisible by only itself and 1. Hence, a contradiction.

Q.E.D

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