Determinant of GCD Matrix

Let AA be an 16 by 16 matrix, with entries ai,j=gcd(i,j) a_{i,j} = \gcd(i, j ) for 1i,j161 \leq i, j \leq 16 . Calculate the last 3 digits of det(A)\det (A) .

Details and assumptions

det(A) \det(A) refers to the determinant of matrix AA.

gcd(i,j)\gcd(i,j) refers to the greatest common divisor of ii and jj.

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