Question 15
Let $n$ be the number
$$\bigl(\underbrace{999\cdots999}_{2006\text{ nines}}\bigr)^2-\bigl(\underbrace{666\cdots666}_{2006\text{ sixes}}\bigr)^2.$$
Find the remainder when $n$ is divided by $11$.
$$\bigl(\underbrace{999\cdots999}_{2006\text{ nines}}\bigr)^2-\bigl(\underbrace{666\cdots666}_{2006\text{ sixes}}\bigr)^2.$$
Find the remainder when $n$ is divided by $11$.