IMO 1992 LL MON49

Given real numbers xi (i = 1, 2, . . . , 4x + 2) such that

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IMO 1992 LL MON49

Origin: MON

Problem

Given real numbers xi (i = 1, 2, . . . , 4x + 2) such that 4x+2  i=1 (−1)i+1xixi+1 = 4m (x1 = x4k+3), prove that it is possible to choose numbers xk1, . . . , xk6 such that 6 The problem in this formulation is senseless. The correct formulation could be, “Find . . . such that \infty m=1 / n m − / n−1 m 0 = 1992 . . . .”  i=1 (−1)6xk1xkk+1 > m (xk1 = xk7).