IMO 1983 LL POL49

Given positive integers k, m, n with km \leqn and nonnegative

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IMO 1983 LL POL49

Origin: POL

Problem

Given positive integers k, m, n with km \leqn and nonnegative real numbers x1, . . . , xk, prove that n k

i=1 xm i −1 \leqm k  i=1 (xn i −1) .