An application for zeroless squares

[Paul C. Leopardi]

Thanks Gordon,
I think that clears it up for me.
On Sat, 30 Apr 2005 12:23 pm, Gordon Royle wrote:
> If it were a crossword, then there would be 2 x n rather boring clues...
...
> The "not starting with zero" comes from this line in the original
> description...
>
> >> Important for solving this puzzle is to omit zeros at the first
> >> position.
>
> Just as in a crossword, where one letter goes in each square, we are
> allowed one digit per square only...
...
> (It took me a few minutes to unpack it all as well..)

OK, so in binary, there is only one solution for 1 x 1, and no solutions for 
n>1 since there are no squares of the form 2^n-1 for n>1.
In ternary, we have
1

1 1
1 1

Any other solutions? Probably very few?

In octal, we have at least
1

4

1 1
1 1

3 1
1 1

4 4
4 4

6 1
1 1

Any others? Probably very many?

In base m^2-1, we always have
1

1 1
1 1
since m^2 is represented as 11 in base m^2-1.


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