After I wrote each of the first n pos- itive integers on a different card, I...

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After I wrote each of the first n pos- itive integers on a different card, I split these cards into three piles (which may or may not contain dif- ferent numbers of cards). For how many distinct values of n 2022 can the numbers written on the cards in each pile have the same sum? After I wrote each of the first n pos- itive integers on a different card, I split these cards into three piles (which may or may not contain dif- ferent numbers of cards). For how many distinct values of n 2022 can the numbers written on the cards in each pile have the same sum?