Wanna bash it! 2

Algebra Level 5

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

Let \(a,b,c\) and \(d\) be complex numbers satisfying the system of equations above. Given that

\[ \displaystyle a^{2015}+b^{2015}+c^{2015}+d^{2015}=2^p+2^q+r ,\]

where \(p,q\) and \(r\) are integers, with \(|r| \) minimized, find \(p+q+r\).


Also try my previous problem.

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