More digital silliness

[David W. Cantrell]

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

I suppose that may be true if you are restricted to the decimal 
system, but DWW said nothing about such a restriction. Using an 
appropriate base, all rotations of 1111 are square, and of course, 
using that same base, so are all rotations of 4444.

David W. Cantrell

> 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? 




Make that 10^18.

Bob


On Jan 9, 2008, at 3:24 PM, Bob Hearn wrote:

> 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?
>