# AIME 1986 problem

Algebra Level 4

The polynomial $$1 - x + x^2 - x^3 + \ldots +x^{16} - x^{17}$$ may be written in the form:

$a_0 + a_1y + a_2y^2 + \ldots +a_{16}y^{16} + a_{17}y^{17},$

where $$y=x+1$$ and $$a_i$$ are constants. Find $$a_2$$.

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