Question about determinants.

Suppose you have n numbers of the form (a1+n*a2+n^2*a3+...n^(n-1)*an) where a1, a2, a3, ..., an are all integers in the interval [0,n-1]. Suppose that d divides all of those numbers. Suppose you arrange those a1, a2, a3, ..., an in each row of a matrix. Does d necessarily divide the determinant of that matrix?

Take the definition of the deteriminant.


can't write it here, don't know VB code or whatever
But it's the sum over the permutation group Sn the sign of e multiplied by the product of A subscript i,e(i)

Now all Aij are divisible by d, therefore the sum of numbers of this form is divisible by d.