Statistics › Median and mode › Lists with given mean and median

Maximum size of a special set

High school · ●●●○○ 50 pts

A set S\mathcal{S} of distinct positive integers has the following property: for every integer xx in S\mathcal{S}, the arithmetic mean of the set of values obtained by deleting xx from S\mathcal{S} is an integer. Given that 11 belongs to S\mathcal{S} and that 20022002 is the largest element of S\mathcal{S}, what is the greatest number of elements that S\mathcal{S} can have?

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divisibilitymodular arithmeticarithmetic mean