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Repunits and bases (Posted on 2013-07-24) Difficulty: 3 of 5
112=3 and 1113=13 are prime. However, 11114=85=5*17 and 111115=781=11*71 are not prime. What is the least number n>3 such that the repunit consisting of n 1's in base n is prime?

See The Solution Submitted by Math Man    
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Question re(2): Answer: | Comment 4 of 6 |
(In reply to re: Answer: by Charlie)

Good question, Charlie!


It is obvious to me that only odd values of n need to be checked.

If n = 2k, then ((2k)^(2k))-1 can be factored into
   (((2k)^(k))-1)  *   (((2k)^(k))+1), 
    and x is not going to be prime if k > 1


  Posted by Steve Herman on 2013-07-24 12:53:15
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