Finding U13 Cyclic Numbers: A Faster Way?

[sarah77]

Homework Statement

Is U¹³ cyclic?

The Attempt at a Solution

I know the elements are
{1,2,3,4,5,6,7,8,9,10,11,12}. I have eliminated 1,2,3,4,5 and I am working on 6. I am doing it this way:

60=1
61=6
62=10
63=8
64=9
65=2

..and so on, but I did, for example, 62=36-13=23=10 and that is how I found 10. But when I get into larger numbers it is very time consuming to type, for example, 64=1296-13=1283-13=1270-13...and so on. Does anyone know a faster way to solve these?

 

[Hurkyl]

If you're looking for a remainder, you could use the long division algorithm. Also, you can make use of what you've already found.