[seqfan] Re: Matrix puzzle

Jeremy Gardiner jeremy.gardiner at btinternet.com
Mon Oct 27 22:27:32 CET 2014

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


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
> with a nonzero determinant divisible by each of the nine
> 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.

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