- The fundamental Matrix Factor Elements are;

[0, 3, 6, 9, 14, 16, 17, 18, 19]

The addition table is:

0 2 4 6 8 10 11

2 4 6 8 10 12 13

5 7 9 11 13 15 16

8 10 12 14 16 18 19

The equivalent Matrix Factor Element sets displayed in a way to show

their equivalence.

0 2 2 4 4 5 6 6 7 8 8 8 9 10 11 12 13 10 10 11 12 13 14 15 16 16 18 19

0 3 6 9 14

16 17 18 19

Notice that the addition table has the elements almost but not quite in

numerical order by reading along the reverse diagonals.

Does anyone have any hints for more quickly finding the equivalent

Matrix Factor Element set that can be arranged into an

addition table?

Kermit < kermit@... > - --- Kermit Rose <kermit@...> wrote:
> The fundamental Matrix Factor Elements are;

So it's a set { a_{i,j} : a_{i,j} = a_{1,j} + a_{i,1} if i>1 or j>1 }

> [0, 3, 6, 9, 14, 16, 17, 18, 19]

>

> The addition table is:

>

> 0 2 4 6 8 10 11

> 2 4 6 8 10 12 13

> 5 7 9 11 13 15 16

> 8 10 12 14 16 18 19

In that case, the whole thing becomes trivial.

Sum { 2^{a_{i,1}} } * Sum { 2^{a_{1,j}} } = N

So if N is prime, no such representation exists.

Phil

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