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

Home > Just Math
Looks like Cauchy (Posted on 2019-04-17) Difficulty: 3 of 5
For all positive integers k, define f(k)=k2+k+1. Compute the largest positive integer n such that


No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Weak solution | Comment 2 of 3 |

The ratio of these values forms a nice pattern:
k=1, 3/1
k=2, 7/3
k=3, 13/7
k=4, 21/13
k=5, 31/21

So the product of these is just the last numerator, which we need to be at most 2019.  Continuing the table

k=44, 1981/1893 (smaller)
k=45, 2071/1981 (too big)

Without looking too hard into why this works, the solution is n=44

  Posted by Jer on 2019-04-18 11:07:17
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 (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information