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equal sums in 2 sets with consecutive positive integers

Source: 2011 Saudi Arabia Pre-TST November 1.1

January 1, 2022
number theoryconsecutive

Problem Statement

Set AA consists of 77 consecutive positive integers less than 20112011, while set BB consists of 1111 consecutive positive integers. If the sum of the numbers in AA is equal to the sum of the numbers in BB , what is the maximum possible element that AA could contain?
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