2004 AIME I Problem 13

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.