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A contains a perfect square

Source: Baltic Way 2008, Problem 11

November 23, 2008
number theory unsolvednumber theory

Problem Statement

Consider a subset AA of 8484 elements of the set {1, 2, …, 169}\{1,\,2,\,\dots,\,169\} such that no two elements in the set add up to 169169. Show that AA contains a perfect square.
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