$($b$)$ Let n $=$ p$1$i$1$ p$2$i$2$ p$3$i$3,$ where p$1,$ p$2,$ p$3$ are distinct primes and i$1,$ i$2,$ i$3$ are positive integers. Write the formula for $\backslash$phi $($n$)$ in a way that shows it$$s a positive integer. Note: Since inclusion$-$exclusion involves adding and subtracting terms, it$$s not clear why the final value is positive; as you compute N$0,$ N$0$N$1,$ N$0$N$1+$N$2,...,$ it can be negative at intermediate steps. We also have a product formula $\backslash$phi $($n$)=$ n$(11/$p$1)(11/$p$2)(11/$p$3)$ with fractions, so it$$s not obvious that it$$s an integer. Rewrite this product formula in a way that shows it$$s a positive integer, and explain why the formula shows that