What Are the Divisibility Patterns of Repunit Numbers?

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SUMMARY

This discussion focuses on the divisibility patterns of repunit numbers, specifically those with an even or odd number of digits. For even-digit repunits, factors can be expressed as products of (11) and other terms, such as (101) or (10101). In contrast, odd-digit repunits present challenges, particularly when the count of digits is prime, as seen in examples like 111 = (3)(37) and 11111 = (41)(271). The conversation emphasizes the need for an algorithm to factor the series represented by 1 + 10 + 10^2 + ... + 10^(2n-1), directing users to search for "repunit numbers" for further information.

PREREQUISITES
  • Understanding of number theory, specifically divisibility rules
  • Familiarity with repunit numbers and their properties
  • Basic knowledge of prime factorization techniques
  • Experience with mathematical series and summation notation
NEXT STEPS
  • Research algorithms for factoring repunit numbers
  • Explore the properties of prime numbers in relation to repunits
  • Study the mathematical series 1 + 10 + 10^2 + ... + 10^(2n-1)
  • Investigate existing literature on divisibility patterns in number theory
USEFUL FOR

Mathematicians, number theorists, and students interested in advanced divisibility concepts and the properties of repunit numbers.

l-1j-cho
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Hello all :)

I am studying divisibilities of
1, 11, 111, 1111, 11111 and so on
when I have even number of 1s, in other words, even number digits
obviously the numers can be factors as (11)(101) , (11)(10101), (11)(1010101)
but when I have odd number of 1s, it is pretty hard if that number is prime
for instance, 111=(3)(37), 11111=(41)(271), 1111111=(239)(4649)
can anyone give a lecture of this?

How do I find an algorithm to factor 1+10+10^2+... + 10^(2n-1)?
 
Physics news on Phys.org
Google for repunit numbers. You'll get lots of results.
 
Petek said:
Google for repunit numbers. You'll get lots of results.

cheers!
 

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