All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
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    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips 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.

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

  Posted by Ady TZIDON on 2013-07-24 15:36:40
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information