# More problems in 2016 part 4. My 400 followers problem.

Let $${f(x)}$$ be a monic cubic polynomial such that ;

$${f(1)=14}$$ , $${f(3)=46}$$ and $${f(5)=150}$$

Let the integral value of $$({f(8)+f(9)+f(10)})$$ be $$H$$

Then evaluate : $$\displaystyle {\left ( \sum_{d\mid H}\frac{1}{\phi (d)} \right )}$$ = $$\frac{p}{q}$$

where $$p$$ and $$q$$ are coprime positive integers, find $$(p-q)-214$$

where $$\phi(q)$$ denote the Euler's totient function.

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