Problem to Brilliant! 7

Algebra Level 4

{a+b+c=9a2+b2+c2=99a3+b3+c3=999 \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,ba,b and cc are complex numbers that satisfy the system of equations above, find the remainder of a5+b5+c5a^5+b^5+c^5 when divided by 78.

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