But it's so large!

Algebra Level 5

\[ \large{ \begin{cases} {a+b+c+d=3} \\ {a^2+b^2+c^2+d^2=5} \\ {a^3+b^3+c^3+d^3=3} \\ {a^4+b^4+c^4+d^4=9} \end{cases} } \]

Given that \(a,b,c\) and \(d\) are complex numbers that satisfy the equation above. If \(a^{2015} + b^{2015} + c^{2015} + d^{2015} \) can be written as \(p^q + p^r - 1\) for positive integers \(p,q,r\), evaluate \(p+q+r+1\).

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