More digital silliness

[Jack Brennen]

Jack Brennen wrote:
> 
> Since it appears that base 10 may not have any solutions, or
> at least none which are easy to find, perhaps there are
> some elegant solutions in other bases?
> 

A really pretty one in base 14
(all representations in base 14 of course):

408^2 = 124848
59D^2 = 248481
804^2 = 484812





This is a cute pair (but still only a pair):

1222222222^2 =  1493827159950617284,
2222222221^2 =  4938271599506172841,

rotating the result by one place.

And here's a solution in base 23:

59L^2 = 16B964,
BL3^2 = 6416B9,
G4B^2 = B96416.

Bob



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?