Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

Photo
- - - - -

(n3+1)/(mn-1)


  • Please log in to reply
5 replies to this topic

#1 plasmid

plasmid

    Senior Lolcat

  • VIP
  • PipPipPipPip
  • 1360 posts
  • Gender:Male

Posted 07 July 2014 - 07:05 AM

Find all pairs of positive integers m and n such that (n3+1) / (mn-1) is an integer, and prove you've identified them all.

 

 

This was a problem I solved back in high school with a proof that could barely fit on one page, written front and back, with small handwriting.

Even looking at it again now, the most elegant proof I can come up with is still pretty complex, but nevertheless sort of neat.

In part, I'm sharing a tricky problem. In part, I'm wondering if there's a more elegant way of solving it than the one I came up with.


  • 0

#2 phil1882

phil1882

    Senior Member

  • Members
  • PipPipPipPip
  • 529 posts

Posted 07 July 2014 - 03:10 PM

Spoiler for the first half, no proof

  • 0

#3 k-man

k-man

    Advanced Member

  • Members
  • PipPipPip
  • 434 posts
  • Gender:Male

Posted 07 July 2014 - 05:21 PM

Spoiler for more numbers than Phil, but still no proof

  • 0

#4 k-man

k-man

    Advanced Member

  • Members
  • PipPipPip
  • 434 posts
  • Gender:Male

Posted 07 July 2014 - 09:29 PM

I don't have the time to put together a complete proof, but here is how I would go about it...

 

Spoiler for outline of the proof

  • 0

#5 plasmid

plasmid

    Senior Lolcat

  • VIP
  • PipPipPipPip
  • 1360 posts
  • Gender:Male

Posted 08 July 2014 - 04:30 AM

I'll say that that approach would certainly be a different way of going about it than what I did.

Spoiler for Before pursuing that approach much further


  • 0

#6 k-man

k-man

    Advanced Member

  • Members
  • PipPipPip
  • 434 posts
  • Gender:Male

Posted 08 July 2014 - 03:02 PM

:duh: So much for a "proof in a hurry" LOL


  • 0




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users