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IMC 2015 · Problem 4

Day 122nd IMC · Blagoevgrad, Bulgaria

Statement

Determine whether or not there exist 15 integers m1,…,m15m_1, \ldots, m_{15} such that

∑k=115mk⋅arctan⁡(k)=arctan⁡(16).(1)\sum_{k=1}^{15} m_k \cdot \arctan(k) = \arctan(16). \tag{1}

Official solution

Hidden so you can work on the problem first.

Proposed by Gerhard Woeginger, Eindhoven University of Technology.