# Problem to Brilliant! 7

Algebra Level 4

$\large \begin{cases} {a+b+c=9} \\ {a^2+b^2+c^2=99} \\ {a^3+b^3+c^3 = 999} \end{cases}$

If $$a,b$$ and $$c$$ are complex numbers that satisfy the system of equations above, find the remainder of $$a^5+b^5+c^5$$ when divided by 78.

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