# 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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