perplexus.info :: Numbers : Repunits and bases

Repunits and bases (Posted on 2013-07-24)

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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re(2): Answer: for any composite, odd or even

| Comment 5 of 6 |

(In reply to re: Answer: by Charlie)

Ch & SH,

Take a composite n like 15 (I have chosen an odd number).

A repunit of 15 ones looks like 111 111 111 111 111 (spaces

introduced to illustrate my point)

or like 11111 11111 11111, and now you see that it is divisible by 111 and by 11111 in any base.

QED

For formal proof replace 15=5*3 by n=p*q

Posted by Ady TZIDON on 2013-07-24 15:36:40

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