Mock AIME 4 2006-2007 Problems/Problem 3

Problem

Find the largest prime factor of the smallest positive integer $n$ such that $r_1, r_2, \ldots , r_{2006}$ are distinct integers such that the polynomial $(x-r_{1})(x-r_{2})\cdots (x-r_{2006})$ has exactly $n$ nonzero coefficients.

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Mock AIME 4 2006-2007 Problems/Problem 3

Problem

Solution