EGMO 2021 Problem 1

Day 1

According to Anna, the number 2021 is fantabulous. She states that if any element of the set $\{m, 2 m+1,3 m\}$ is fantabulousfor a positive integer $m$ , then they are all fantabulous. Is the number 2021 ${ }^{2021}$ fantabulous? (Australia, Angelo Di Pasquale)

Dataset text NuminaMath olympiads. Quoted with source.

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