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I have been reading a book with an introductory section on number theory and the part regarding Euler's function just said that [tex] \varphi (n) = n-1 [/tex] when n is prime and that [tex] \varphi (n) = n(1-\frac{1}{p_{1}})(1-\frac{1}{p_{2}})...(1-\frac{1}{p_{n}}) [/tex] when n is a composite number.

The book (What is mathematics by Richard Courant) said the proof was "completely trivial" but that they wouldn't say it and I was wondering if someone could provide a proof or guide me through one.

Thanks in advance.

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# Proof of Euler's fuction.

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