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Combinatorics-Number Theory problem

Source: Moldova TST 2018

April 6, 2018
combinatoricsnumber theory

Problem Statement

Let the set A=A={1,2,3,…,48n+24 1,2,3, \dots ,48n+24 } , where n∈N∗ n \in \mathbb {N^*} . Prove that there exist a subset BB of AA with 24n+1224n+12 elements with the property : the sum of the squares of the elements of the set BB is equal to the sum of the squares of the elements of the set AA \ BB .
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