Euler's totient function: Difference between revisions

Revision as of 09:55, 18 July 2025

Revision as of 09:56, 18 July 2025

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:<math> \frac{\varphi(n)}{n} = \frac{p_1-1}{p_1}\frac{p_2-1}{p_2} \cdots \frac{p_r-1}{p_r} </math>

and this holds for any integersinteger, whatever the power <math> p_r^{\alpha_r} </math> of the primes in the prime decomposition. Therefore all the prime numbers <math> n= p </math>, or the simple power of a prime number like <math> n= p^\alpha </math> lead to

:<math> \frac{\varphi(n)}{n} = \frac{p-1}{p} </math>