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.
For diagonal elements all = d and all other elements = 1,
for n greater than or equal 3:
for n odd:
det(Mn) = d^n - n d + (n-1)
for n even:
det(Mn) = d^n - (n/2) d^2 + (n/2 -1)
(this is a start)