Finding U13 Cyclic Numbers: A Faster Way?

In summary, a cyclic number is a number that, when multiplied by any of its digits, produces a new number that is a cyclic permutation of the original number. Finding U13 cyclic numbers is significant because they have unique mathematical properties and are useful in applications such as cryptography and number theory. The current method for finding U13 cyclic numbers is time-consuming and involves checking each number individually. The faster way of finding U13 cyclic numbers uses a mathematical algorithm that takes advantage of the unique properties of U13 cyclic numbers to reduce the time and effort needed to find them. This can lead to potential applications in fields such as cryptography, number theory, and computer science, as well as the discovery of new mathematical properties and relationships among U13 cyclic numbers.
  • #1
sarah77
27
0

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?
 
Physics news on Phys.org
  • #2
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.
 

FAQ: Finding U13 Cyclic Numbers: A Faster Way?

What is a cyclic number?

A cyclic number is a number that, when multiplied by any of its digits, produces a new number that is a cyclic permutation of the original number. For example, the number 142857 is a cyclic number because when multiplied by 2, it becomes 285714, which is a permutation of the original number.

What is the significance of finding U13 cyclic numbers?

Finding U13 cyclic numbers is significant because these numbers have unique mathematical properties that make them useful in various applications, such as in cryptography and number theory. They are also rare and difficult to find, so discovering a faster way to find them can greatly benefit mathematical research.

What is the current method for finding U13 cyclic numbers?

The current method for finding U13 cyclic numbers involves checking each number individually, which is a time-consuming process. This method is known as brute force and can take a long time to find even one U13 cyclic number.

How does the faster way of finding U13 cyclic numbers work?

The faster way of finding U13 cyclic numbers uses a mathematical algorithm that can quickly identify potential U13 cyclic numbers without having to check each number individually. This algorithm takes advantage of the unique properties of U13 cyclic numbers to greatly reduce the time and effort needed to find them.

What are the potential applications of the faster way of finding U13 cyclic numbers?

The faster way of finding U13 cyclic numbers can have various applications in fields such as cryptography, number theory, and computer science. It can also potentially lead to the discovery of new mathematical properties and relationships among U13 cyclic numbers.

Similar threads

Final Grades for Linear Algebra Course
Replies
3
Views
2K
MCNP Tally f8 unreliable since neutron transport is nonanalog
Replies
3
Views
2K
B Finding all possible sums given 2 lists, matched one to one
Replies
2
Views
1K
A Number of unequal integers with sum S
Replies
12
Views
1K
B Transferring information faster than the speed of light
Replies
24
Views
1K
How Does Sum of Consecutive Numbers Relate to Cubes of Integers?
Replies
2
Views
1K
Can You Decode This List of Numbers into a Message?
Replies
18
Views
12K
Frequency Distribution Width & 'Rounding Up'
Replies
4
Views
5K
Test concerning difference of two means
Replies
2
Views
2K
How many cards can be taken at most while satisfying a certain rule?
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top