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QUESTION

List those residues mod 15 which are coprime with 15. Hence write
down the value of $\phi(15)$ and check it against the formula
obtained in cor.5.4.



ANSWER

We must omit all multiples of 3 and 5, so the remains residues are
1,2,4,7,8,11,13,14 showing that $\phi(15)=8$. The formula gives
$\phi(15)=15\left(1-\frac{1}{3}\right)\left(1-\frac{1}{5}\right)=15\left(\frac{2}{3}\right)\left(\frac{4}{5}\right)=8$,
agreeing with our previously obtained value.




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