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Division in parts inversely proportional to some numbers

Source: Paraguayan National Olympiad 2011, Level 3, Problem 4

August 31, 2014
algebra proposedalgebra

Problem Statement

A positive integer NN is divided in nn parts inversely proportional to the numbers 2,6,12,20,…2, 6, 12, 20, \ldots The smallest part is equal to 1400N\frac{1}{400} N. Find the value of nn.
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