IMO 1988 LL GRE29

Find positive integers x1, x2, . . . , x29, at least one of which is

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IMO 1988 LL GRE29

Origin: GRE

Problem

Find positive integers x1, x2, . . . , x29, at least one of which is greater than 1988, such that x2 1 + x2 2 + \cdot \cdot \cdot + x2 29 = 29x1x2 . . . x29.