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