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Algebra Level 4

a+b+c=1a2+b2+c2=2a3+b3+c3=3a5+b5+c5=? \begin{array} { l l l l l l l l l } a & + & b & + & c & = & 1 \\ a^2 & + & b^2 & + & c^2 & = & 2 \\ a^3 & + & b^3 & + & c^3 & = & 3 \\ a^5 & + & b^5 & + & c^5 & = & ? \\ \end{array}

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