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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