Polynomials and more polynomials?

Algebra Level 5

Let \(Q_{n+1}(x)=Q (Q _{n}(x)), Q_{1}(x)=Q (x)\) for all positive integers \(n\).

Consider all polynomials \(Q (x)\) with integer coefficients such that \(Q_{2015} (x)-x\) has a positive integer root \(p\). Find the minimum value of \((p+1)^{2}-Q_{2014}(p)\) .

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