# There must be a simpler way

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.

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

×