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

Home > Just Math
Harmonic Integers (Posted on 2006-02-07) Difficulty: 3 of 5
Given that, a, b, and c are all positive integers so that a < b < c, and 1/a, 1/b, and 1/c are in arithmetic progression, can a + b be equal to c?

See The Solution Submitted by K Sengupta    
Rating: 2.2000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): I think I have it | Comment 3 of 5 |
(In reply to re: I think I have it by Eric)

"Maybe you meant to set 1/b + k = 1/c and 1/a +2k = 1/c."

That's right Eric, that's exactly what I did - I just posted it wrong.  I fixed my post.  Thanks for catching this.

"Also, I don't think k has to be an integer, it just has to be rational."

I suppose there might be other definitions of "arithmetic progression" out there, but the one I'm looking at shows that k must be an integer (CRC Concise Encyclopedia of Mathematics, Eric W. Weisstein, 1999).

  Posted by Mindrod on 2006-02-08 09:30:19
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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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