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Difference of sum of squares of parts of a bipartition

Source: KAMO 2022 Grade 9 P3

July 5, 2022

number theory

Problem Statement

Is it possible to partition

\{1, 2, 3, \ldots, 28\}

into two sets

A

and

B

such that both of the following conditions hold simultaneously:
(i) the number of odd integers in

A

is equal to the number of odd integers in

B

;
(ii) the difference between the sum of squares of the integers in

A

and the sum of squares of the integers in

B

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