What Are the Divisibility Patterns of Repunit Numbers?

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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)?
 
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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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