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Partition of set {1,2,3...4mn} so that every sum is a square

Source: Romanian TST 2002

February 5, 2011
number theory proposednumber theory

Problem Statement

Let m,nm,n be positive integers of distinct parities and such that m<n<5mm<n<5m. Show that there exists a partition with two element subsets of the set {1,2,3,…,4mn}\{ 1,2,3,\ldots ,4mn\} such that the sum of numbers in each set is a perfect square.
Dinu Șerbănescu
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