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?

Not a pro at linear mathematics, but I don't believe that' (a1, a2, a3, ...)/d = (detA)/d.  You could test this rather simply by simply limiting your set to a small matrix greater than 1x1, dividing all members by d and summing them, then finding the determinate and dividing by d.  If they're not equal, it's not a rule.