Let $D$ be the largest divisor of $1001001001$ that does not exceed $10000$. Find the remainder when $D$ is divided by $7$.
Let $S = \{2006, 2007, 2008, \ldots, 4012 \}$. Let $K$ denotes the sum of the greatest odd divisor of each of the element of $S$. Find the value of $K$.
I don't understand how to solve this question. I have been trying hard to solve them.