I was wondering a problem: Is it possible to construct a $$$n \times n$$$ matrix (call it A) such that each number from $$$1$$$ to $$$n$$$ appears exactly $$$n$$$ times and the result of $$$A \times A$$$ (matrix multiplication) is a zero matrix (after modulo $$$n \times n$$$ terms in the matrix by $$$n$$$). I know it is obvious for odd $$$n$$$ but how about even $$$n$$$?
Upd: After roughly 2 weeks the solution is done by Phd Ben Grossmann and Litho on math stackexchange. You can find the solution and proof here. Thanks div4only for providing me with great support. I will state the construction here only.
Satisfied matrix construction
I do not know if this contributes much to competitive programming, but it is fun doing these types of math problems.
