IME - Combinatorics

The coefficients $$a_{0}$$, ..., $$a_{2004}$$ of the polynomial $$P(x)=x^{2015}+a_{2014}x^{2014}+...+a_{1}x+a_{0}$$ are such that $$a_{i} \in \{0,1\}$$, for $$0\leq i \leq 2014$$. The number of these polynomials which admit two distinct integer roots can be written as $$\displaystyle {a \choose b}$$, with $$b > a-b$$. Determine the value of $$a-b$$.

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