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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