[seqfan] Re: Need help finding prime index values for sequence A363381
Thomas Young
tomyoungmathman at gmail.com
Thu Aug 17 04:19:40 CEST 2023
Thomas,
Thanks for your insights. I'm not sure I agree but I don't have a
counter-argument. Does this take into consideration the n X n arrays such
as 1575 X 1575 = 3*3*5*5*7 X 3*3*5*5*7? Given the number of odd factors,
there will be several f1 X f2 blocks that fill the array
Does anyone else have insights on this topic?
On Wed, Aug 16, 2023 at 6:25 AM Thomas Scheuerle <ts181 at mail.ru> wrote:
> Hello,
>
> I expect that it is already very difficult to find solutions for any odd n.
> Why ?
> I observed that most solutions can be found with some approach:
> First we start with shapes identical to rows or columns.
> If we then apply individual permutations inside rows and inside columns
> such that each
> of these permutations moves all elements the same absolute distance, then
> this approach can find solutions.
> If we investigate this case then we find that such permutations are
> generally even.
> That means they are a product of an even number of independent element
> swaps and can therefore only exist over
> an even number of elements.
> Therefore I conjecture if only solutions exist which can be reached by
> such permutations, then
> The only solutions for odd p in a p x p matrix will be rows or columns as
> shapes.
>
> Best regards
>
> Thomas
>
--
Tom Young
Executive Director
Minnesota State HS Math League
Math Teacher, Spring Lake Park HS, retired
763-568-0118
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