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Find s(n)

Source: INMO 1991 Problem 10

October 3, 2005

Problem Statement

For any positive integer nn , let s(n)s(n) denote the number of ordered pairs (x,y)(x,y) of positive integers for which 1x+1y=1n\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{n} . Determine the set of positive integers for which s(n)=5s(n) = 5
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