Question 10
An $n \times n$ table contains the numbers $1,2, \ldots, n^{2}$, each exactly once. Call it a Niš table if the product of the $n$ entries in any $n$ cells, no two in the same row or column, has the same remainder modulo $n^{2}+1$. Does such a table exist for:
a. $n=8$;
b. $n=10$?
(Such a selection of $n$ cells is called scattered.)
a. $n=8$;
b. $n=10$?
(Such a selection of $n$ cells is called scattered.)