Let $p$ be a polynomial of minimal degree to which the following is true:
$p(0) > \sum\limits_{i=1}^n \lvert p(i) \rvert + \sum\limits_{i=1}^m \lvert p(-i) \rvert$
Give upper and lower bounds for $deg(p)$ (for sufficently large $n$).
I constructed bounds for $p(0) > \sum\limits_{i=1}^n \lvert p(i) \rvert$ using Chebyshev-polynomials, which is $c_1\sqrt{n} < deg(p) < c_2\sqrt{n}$, where $c_1$ and $c_2$ are constants. However, I'm having trouble with both sums.