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

Home > Just Math
Reciprocal Period Poser (Posted on 2016-10-29) Difficulty: 3 of 5
N is a duodecimal positive integer ≤ BB.
Find the value of N such that 1/N has the maximum period of its digits after the duodecimal point.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
solution | Comment 1 of 2
let N=2^a*3^b*k where k is not divisible by 2 or 3

Then the duodecimal representation of 1/N is given by a series of R digits and then a repeating series of L digits where
L is the smallest positive integer such that 12^L = 1 mod k

now this L is maximized for prime k and we get the largest k for when N itself is prime.  Thus we want the largest prime less than BB (143) which is 139

thus the maximum period is 138 when N=B7

  Posted by Daniel on 2016-10-29 09:51:37
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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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