Question 117
Let $1 \lt t \lt 2$ be a real number. Prove that for all sufficiently large positive integers $d$, there is a monic polynomial $P(x)$ of degree $d$, such that all of its coefficients are either $+1$ or $-1$ and
$$
|P(t) - 2019| \lt 1.
$$
$$
|P(t) - 2019| \lt 1.
$$