MathDB
Roots of Unity

Source:

December 20, 2005

Problem Statement

Let vv and ww be distinct, randomly chosen roots of the equation z19971=0.z^{1997}-1=0. Let m/nm/n be the probability that 2+3v+w,\sqrt{2+\sqrt{3}}\le |v+w|, where mm and nn are relatively prime positive integers. Find m+n.m+n.