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

Home > Just Math
Oblong Difference Observation (Posted on 2015-10-15) Difficulty: 3 of 5
Find all possible pairs (M, N) of oblong numbers that satisfy:

M - N = 2016

Prove that there are no others.

*** As an extra challenge solve this puzzle without using a computer program aided method.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
solution | Comment 1 of 3
I've never heard of oblong numbers before but using the linked definition M=m(m+1) and N=n(n+1).

Substitute into M-N=2016, multiply by 4, add and subtract 1 to get
(2m+1)^2 - (2n+1)^2 = (2m+2n+2)(2m-2n) = 8064 = (2^7)(3^2)(7) with solutions (m,n)=(47,15),(58,37),(116,107),(1008,1007).

Then solutions (M,N)=(2256,240),(3422,1406),(13572,11556), (1017072,1015056).

  Posted by xdog on 2015-10-15 12:48:34
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