## Spring 2018, problem 69

It is known that $k$ and $n$ are positive integers and [ k + 1\leq\sqrt {\frac {n + 1}{\ln(n + 1)}}.] Prove that there exists a polynomial $P(x)$ of degree $n$ with coefficients in the set $\{0,1, - 1\}$ such that $(x - 1)^{k}$ divides $P(x)$.