An Odd Cycle Argument

Problem

The set A={1011,1012,,2022}A = \{1011, 1012, \dots, 2022\} is partitioned arbitrarily into two disjoint nonempty subsets. Prove that at least one of the subsets contains two numbers whose sum is a perfect square.

Answer

Solution

Difficulty7/10
Topicscombinatorics, Graph Theory, number theory, Pigeonhole

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