It must be 7!

Level pending

\[ a+b+c=1 \\ a^3+b^3+c^3=3 \\ a^5+b^5+c^5=5 \]

Let \(a,b,c\) be complex numbers satisfying the equations above. What is the value of \(a^7+b^7+c^7 \) round up to the closest integer?

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