Problem

Source: Moldova TST 2018

Tags: combinatorics, number theory



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