# Vieta's is the easy part

A quartic polynomial has the very interesting property that the coefficient of $$x^{ n }$$ for $$n=0,1,2,3,4$$ is given by $$\displaystyle \sum _{ j=1 }^{ n+1 }{ \sum _{ k=1 }^{ 5 }{ \frac { \phi (k^{ j }) }{ \phi (k) } } }$$.

If the sum of the roots of this polynomial is $$X$$, and the product of the roots of this polynomial is $$Y$$, calculate $$Y-X$$.

If the answer is in the form $$\dfrac { p }{ q }$$ where $$p$$ and $$q$$ are co-prime positive integers, submit your answer as $$p+q+145$$.

Notation: $$\phi (k)$$ denotes the Euler's totient function.

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