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**chisigma** If $\displaystyle n= p_{1}\ p_{2}\ ... p_{k}$ , each $\displaystyle p_{i}, i=1,2,...,k$ prime, then is...

$\displaystyle \varphi(n)= (p_{1}-1)\ (p_{2}-1)\ ... (p_{k}-1) $ (1)

But the only possible factorisation of $\displaystyle \varphi(n)$ is $\displaystyle \varphi(n)=14 = 2*7$ and it exists a prime $\displaystyle p_{1}$ for which is $\displaystyle p_{1}-1=2$ but no prime $\displaystyle p_{2}$ for which is $\displaystyle p_{2}-1=7$...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$