# 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.

×