[seqfan] Re: Matrix puzzle

[Jeremy Gardiner]

Matrix puzzle
Example solution:   6       2       4
                    9       8       1
                    3       10      5
det A = 360

Considering an mxm matrix with all elements k or less
Then I conjecture:

m=2 has no solutions for k < 12
m=3 has no solutions for k < 10
m=4 has no solutions for k < 20

Jeremy

On 26/10/14 00:03, "Charles Greathouse" <charles.greathouse at case.edu> wrote:

> A friend of mine asks: Can you find a 3X3 matrix of distinct positive
integers
> with a nonzero determinant divisible by each of the nine
constituent
> elements?

It's easy to find a matrix with eight of the nine dividing the
> determinant
-- pick (almost) whatever you want for the first eight, then fit
> the last
to give a determinant equal to the product of the others.