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Splitting integers

Source: INMO 1999 Problem 6

October 7, 2005
number theory solvednumber theory

Problem Statement

For which positive integer values of nn can the set {1,2,3,…,4n}\{ 1, 2, 3, \ldots, 4n \} be split into nn disjoint 44-element subsets {a,b,c,d}\{ a,b,c,d \} such that in each of these sets a=b+c+d3a = \dfrac{b +c +d} {3}.
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