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.
det(M4) = d^4 -2 d^2 +1 = (d^2 -1) ^ 2
(A square for all integer d.)
The problem was not that hard after all!
2018 was a red herring I think.
Edited on June 15, 2018, 12:03 pm