Difference between revisions of "Product representation of totient"
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Revision as of 04:43, 22 June 2016
Theorem
The following formula holds for distinct primes $p$ dividing $n$: $$\phi(n)=n \displaystyle\prod_{p | n} \left[ 1 - \dfrac{1}{p} \right],$$ where $\phi$ denotes the totient.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $24.3.2 I.C.$
