MathDB
Sets

Source: AIME 2002 #14

November 28, 2005
AIMEAIME IAIME IIUSASetsmodular arithmetic

Problem Statement

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 1 belongs to S\mathcal{S} and that 2002 is the largest element of S,\mathcal{S}, what is the greatet number of elements that S\mathcal{S} can have?
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