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Sum equals Product

Source: IMO LongList 1988, Greece 4, Problem 24 of ILL

October 22, 2005
algebra unsolvedalgebra

Problem Statement

Find the positive integers x1,x2,…,x29x_1, x_2, \ldots, x_{29} at least one of which is greater that 1988 so that x12+x22+…x292=29⋅x1⋅x2…x29. x^2_1 + x^2_2 + \ldots x^2_{29} = 29 \cdot x_1 \cdot x_2 \ldots x_{29}.
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