MathDB
Subsets, sums and products

Source: JBMO Shortlist 2006

November 10, 2008
combinatorics proposedcombinatorics

Problem Statement

Let n≥5 n\ge 5 be a positive integer. Prove that the set {1,2,…,n} \{1,2,\ldots,n\} can be partitioned into two non-zero subsets Sn S_n and Pn P_n such that the sum of elements in Sn S_n is equal to the product of elements in Pn P_n.
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