For each positive integer n, let Mn be the square matrix (nxn) where each diagonal entry is 2018, and every other entry is 1.

Determine the smallest positive integer n (if any) for which the value
of det(Mn) is a perfect square.

(In reply to computer solution by Charlie)

I notice I'm interpreting diagonal entry differently from the preceding poster; I'm assuming both diagonals, rather than just the main diagonal. I'll have to later try out main diagonal only.

Posted by Charlie on 2018-06-15 07:31:40