# Restriction of coefficients

Algebra Level 5

Find the least positive integer $$n$$, such that there is a polynomial $P(x) = a_{2n}x^{2n}+a_{2n-1}x^{2n-1}+\dots+a_1x+a_0$ with real coefficients that satisfies both of the following properties:

• For $$i=0,1,\ldots,2n$$ it is $$2014 \leq a_i \leq 2015$$.

• There is a real number $$\xi$$ with $$P(\xi)=0$$.

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