A polynomial $p$ with integer coefficients is such that $p(-n) < p(n) < n$ for some integer $n$. Prove that $p(-n) < -n$.
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Tags: inequalities, algebra, polynomial
A polynomial $p$ with integer coefficients is such that $p(-n) < p(n) < n$ for some integer $n$. Prove that $p(-n) < -n$.