IME - Combinatorics

Discrete Mathematics Level pending

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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