International Mathematics Competition
for University Students
2015

IMC2015: Day 1, Problem 4

4. Determine whether or not there exist 15 integers $m_1,\ldots,m_{15}$ such that~ $$\displaystyle \sum_{k=1}^{15}\,m_k\cdot\arctan(k) = \arctan(16). \qquad\qquad(1)$$

Proposed by Gerhard Woeginger, Eindhoven University of Technology

Hint: Use complex numbers and the complex norm.

  Solution