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 $a-b$ .