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 re(2): computer solution by Steven Lord)

My program, if modified, would have the same rounding difficulties as yours. But this may help: 8217949832^2 = 67534699441268828224, so if you did your calculations mod 10000 you could see if the last four digits match those of the square of the square root. 

Posted by Charlie on 2018-06-15 10:11:06