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least no of elements removing from {1,2,...,20} such any 2 sum perfect square

Source: 2011 Belarus TST 8.1

November 8, 2020
number theoryPerfect SquaresPerfect Square

Problem Statement

Find the least possible number of elements which can be deleted from the set {1,2,...,20}\{1,2,...,20\} so that the sum of no two different remaining numbers is not a perfect square.
N. Sedrakian , I.Voronovich