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Polish MO 2022 P5

Source: Polish MO 2022 P5

February 12, 2022
algebranumber theory

Problem Statement

Let nn be an positive integer. We call nn <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> when there exists positive integer kk s.t. n=k(k+1)n=k(k+1). Does there exist 2022 pairwise distinct <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> numbers s.t. their sum is also <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> number?
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