Let n be a positive integer. Mary writes the n3 triples of not necessarily distinct integers, each between 1 and n inclusive on a board. Afterwards, she finds the greatest (possibly more than one), and erases the rest. For example, in the triple (1,3,4) she erases the numbers 1 and 3, and in the triple (1,2,2) she erases only the number 1,Show after finishing this process, the amount of remaining numbers on the board cannot be a perfect square. number theorycombinatorics