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 derivation of the formula by Steven Lord)

very well done, the way I got it was by simply using wolfram alpha to compute the det for the matrix with x in place for the diagonal values and noticed the pattern in the factorization of the resulting polynomial.

Posted by Daniel on 2018-06-16 20:48:52