Let $m$ be the number of integers $n$, $1 \le n \le 2005$, such that the polynomial $x^{2n} + 1 + (x + 1)^{2n}$ is divisible by $x^2 + x + 1$. find the remainder when $m$ is divided by 1000.

The fence around a quadrilateral-shaped pasture is 3a^2+15a+9 long. three sides of the fence have the following lengths: 5a, 10a-2, a^2-7. what is the length of the fourth side of the fence?

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Ana earns 2.5% simple interest on $2,000 in her savings account. she does not make any deposits or withdrawals. after 3 years, how much interest will ana have earned on her savings account?