4

Part of 2015 Bosnia Herzegovina Team Selection Test

Problems(1)

Set of 8 conescutive positive integers

Source: Bosnia and Herzegovina TST 2015 day 2 problem 1

X

be a set which consists from

8

consecutive positive integers. Set

X

is divided on two disjoint subsets

A

B

with equal number of elements. If sum of squares of elements from set

A

is equal to sum of squares of elements from set

B

, prove that sum of elements of set

A

is equal to sum of elements of set

B

combinatoricsSum of Squaresset