# 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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