Question 50
Let $N$ be the smallest positive integer for which
$$
x^{2}+x+1 \quad \text{divides} \quad 166-\sum_{d \mid N, d\gt 0} x^{d}
$$
Find the remainder when $N$ is divided by $1000$.
$$
x^{2}+x+1 \quad \text{divides} \quad 166-\sum_{d \mid N, d\gt 0} x^{d}
$$
Find the remainder when $N$ is divided by $1000$.