Question 141
Let $n$ be a positive integer. We say that a $n \times n$ table is *special* if:
* each cell of the table contains a 2-digit odd positive integer;
* the numbers of the table are pairwise distinct;
* the products of the numbers of each line and the products of the numbers of each column are perfect squares.
Prove that the largest value of $n$ for which there exists a $n \times n$ special table is equal to 4.
* each cell of the table contains a 2-digit odd positive integer;
* the numbers of the table are pairwise distinct;
* the products of the numbers of each line and the products of the numbers of each column are perfect squares.
Prove that the largest value of $n$ for which there exists a $n \times n$ special table is equal to 4.