Difference between revisions of "Product representation of totient"
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(Created page with "==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...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Sum of totient equals z/((1-z) squared)|next=Euler totient is multiplicative}}: $24.3.2 I.C.$ | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Sum of totient equals z/((1-z) squared)|next=Euler totient is multiplicative}}: $24.3.2 \mathrm{I}.C.$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 04:50, 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): $24.3.2 \mathrm{I}.C.$
