The polynomial $$P(x)=(1+x+x^2+\cdots+x^{17})^2-x^{17}$$ has 34 complex roots of the form $$z_k = r_k[\cos(2\pi a_k)+i\sin(2\pi a_k)], k=1, 2, 3,\ldots, 34,$$ with $$0 < a_1 \le a_2 \le a_3 \le \cdots \le a_{34} < 1$$ and $$r_k>0.$$ Given that $$a_1 + a_2 + a_3 + a_4 + a_5 = m/n,$$ where $$m$$ and $$n$$ are relatively prime positive integers, find $$m+n.$$

(第二十二届AIME1 2004 第13题)