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Differences of elements in a set

Source: 2009 AIME I #8

March 18, 2009

modular arithmeticreal analysisAMCAIMEcalculusderivativegeometric series

Problem Statement

Let S \equal{} \{2^0,2^1,2^2,\ldots,2^{10}\}. Consider all possible positive differences of pairs of elements of

S

. Let

N

be the sum of all of these differences. Find the remainder when

N

is divided by

1000