Determine whether or not there exist 15 integers m1,…,m15
such that~
\displaystyle \sum_{k=1}^{15}\,m_k\cdot\arctan(k) = \arctan(16). \eqno(1)(Proposed by Gerhard Woeginger, Eindhoven University of Technology) number theorytrig identitiescollege contestsIMC2015