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Algebra Level 4

Let \({ a }_{ 1 }, { a }_{ 2 }, { a }_{ 3 }, \ldots ,{ a }_{ 17 }\) be the roots of the equation \({ x }^{ 17 }+17x-2015=0\). Find the value of the sum below.

\[ \large { { a }_{ 1 } }^{ 17 }+{ { a }_{ 2 } }^{ 17 }+{ { a }_{ 3 } }^{ 17 }+\cdots +{ { a }_{ 16 } }^{ 17 }+{ { a }_{ 17 } }^{ 17 }\]

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