IMO 1987 LL GRE30

Consider the regular 1987-gon A1A2 . . . A1987 with center O.

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IMO 1987 LL GRE30

Origin: GRE

Problem

Consider the regular 1987-gon A1A2 . . . A1987 with center O. Show that the sum of vectors belonging to any proper subset of M = {OAj | j = 1, 2, . . . , 1987} is nonzero.