Question 103
Let $1 \lt t \lt 2$ be a real number. Show that for any integer $d$ sufficiently large, there is a polynomial $P(X) = \sum_{k=0}^{d} a_{k} X^{k}$, with $a_{d} = 1$ and $a_{0}, \ldots, a_{d-1} \in \{1, -1\}$, such as: $$
|P(t) - 2019| \leqslant 1
$$
|P(t) - 2019| \leqslant 1
$$