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Set of 8 conescutive positive integers

Source: Bosnia and Herzegovina TST 2015 day 2 problem 1

May 18, 2015
combinatoricsSum of Squaresset

Problem Statement

Let XX be a set which consists from 88 consecutive positive integers. Set XX is divided on two disjoint subsets AA and BB with equal number of elements. If sum of squares of elements from set AA is equal to sum of squares of elements from set BB, prove that sum of elements of set AA is equal to sum of elements of set BB.
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