## Problem of the Day #291: Two Hundred Ninety One
*January 4, 2012*

*Posted by Saketh in : potd , trackback*

Consider the function $f(x) = 1-x+x^2-x^3+\cdots-x^{2011}+x^{2012}$. Let $y = x+1$, and suppose we rewrite our expression as the polynomial $g(y)$.

Find the greatest integer $k$ such that $2^k$ evenly divides the coefficient of $y^{291}$ in $g$.

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