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

form of the determinants by Steven Lord)

seems for d=2018 n=4 and n=5, det(Mn) are in fact squares:

4072324^2 and 182937568^2

(computer solution)

I think I need practice finding the roots of polynomials.....