# Is Newton's applicable here too?

Algebra Level 4

$\large { \begin{cases} { a+b =1} \\ {ax+by=2}\\ {ax^{2}+by^{2}=-6}\\ {ax^{3}+by^{3}=8}\\ \end{cases} }$ We are given that $$a,b,x,$$ and $$y$$ are complex number that satisfy the system of equations above.

if $$ax^{2015}+by^{2015}$$ can be written as $$p\cdot q^{r}$$ for integers $$p,q,r$$ with $$q,r$$ primes, evaluate $$p+q+r$$.

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