Finding U13 Cyclic Numbers: A Faster Way?

  • Thread starter Thread starter sarah77
  • Start date Start date
  • Tags Tags
    Cyclic Numbers
Click For Summary
SUMMARY

The discussion focuses on finding U13 cyclic numbers using a more efficient method than manual calculations. The user has identified elements {1,2,3,4,5,6,7,8,9,10,11,12} and has begun eliminating numbers through a method involving modular arithmetic. They suggest using the long division algorithm to expedite the process of finding remainders, which is crucial for determining cyclicity. The conversation emphasizes the need for a systematic approach to handle larger numbers effectively.

PREREQUISITES
  • Understanding of cyclic numbers and their properties
  • Familiarity with modular arithmetic concepts
  • Knowledge of the long division algorithm
  • Basic skills in number theory
NEXT STEPS
  • Research advanced techniques in modular arithmetic
  • Explore algorithms for generating cyclic numbers
  • Study the properties of U13 cyclic numbers in detail
  • Learn about optimization strategies for number theory problems
USEFUL FOR

Mathematicians, students studying number theory, and anyone interested in optimizing calculations involving cyclic numbers.

sarah77
Messages
27
Reaction score
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
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.
 

Similar threads

Final Grades for Linear Algebra Course
  • · Replies 3 ·
Replies
3
Views
3K
Graduate About a natural extension of Collatz conjecture
  • · Replies 3 ·
Replies
3
Views
1K
MCNP Tally f8 unreliable since neutron transport is nonanalog
  • · Replies 3 ·
Replies
3
Views
4K
High School Finding all possible sums given 2 lists, matched one to one
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Number of unequal integers with sum S
  • · Replies 12 ·
Replies
12
Views
2K
How Does Sum of Consecutive Numbers Relate to Cubes of Integers?
  • · Replies 2 ·
Replies
2
Views
2K
High School Transferring information faster than the speed of light
  • · Replies 24 ·
Replies
24
Views
4K
Can You Decode This List of Numbers into a Message?
  • · Replies 18 ·
Replies
18
Views
15K
Frequency Distribution Width & 'Rounding Up'
  • · Replies 4 ·
Replies
4
Views
6K
Test concerning difference of two means
  • · Replies 2 ·
Replies
2
Views
2K