More digital silliness

[Maximilian Hasler]

On Jan 9, 2008 3:33 PM, David W. Wilson <wilson.d at anseri.com> wrote:
>
> Let an n-digit number be valid if it does not start or end with 0.

(*below n is no more the number of digits...*)

> Let a rotation of n be gotten by rotating its digits. Thus the rotations of
> 256 are 256, 562 and 625.
> Is there a number with more than two valid square rotations?

Well, the squares of
245,247,1249,2498,3743,9078,...
do not start or end with 0,  but the rotated ones do...

Maximilian



There's probably some simple reason that the answer is no, but  
empirically, there are no such numbers < 10^16.

Bob Hearn


On Jan 9, 2008, at 2:33 PM, David W. Wilson wrote:

> Let an n-digit number be valid if it does not start or end with 0.
>
> Let a rotation of n be gotten by rotating its digits. Thus the  
> rotations of 256 are 256, 562 and 625.
>
> We note that 256 has two valid square rotations, 256 and 625.
>
> Is there a number with more than two valid square rotations?