Polynomials and more polynomials?

Algebra Level 5

Let Qn+1(x)=Q(Qn(x)),Q1(x)=Q(x)Q_{n+1}(x)=Q (Q _{n}(x)), Q_{1}(x)=Q (x) for all positive integers nn.

Consider all polynomials Q(x)Q (x) with integer coefficients such that Q2015(x)xQ_{2015} (x)-x has a positive integer root pp. Find the minimum value of (p+1)2Q2014(p)(p+1)^{2}-Q_{2014}(p) .

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