puzzles (8-15-08)

[Christopher Wright]

Wyverex wrote:
> 1)  Consider the number 142857. We can right-rotate this number by 
> moving the last digit (7) to the front of it, giving us 714285.
> It can be verified that 714285=5*142857.
> This demonstrates an unusual property of 142857: it is a divisor of its 
> right-rotation.
> 
> Find the digits of the set of all integers n, 11 < n < 10^100, that have 
> this property.
> 
> 
> 
> 2 and 3 from the other day are time consuming but are good practice for 
> new programmers!

10^100 is greater than ulong.max.

I tried a version that went up to ulong.max. It logged every billion 
checks. That took a few minutes (for the first billion, I mean). Getting 
all the way to ulong.max would take overnight; to 10^100, ages, even if 
you had a ucent primitive.

Granted, I was using ulongs on my 32-bit machine, so it wasn't optimal. 
But bignums are a lot slower.