Is Newton's applicable here too?

$\large { \begin{cases} { a+b =1} \\ {ax+by=2}\\ {ax^{2}+by^{2}=-6}\\ {ax^{3}+by^{3}=8}\\ \end{cases} }$ 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 $p+q+r$ .