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

Home > Just Math
Cubic Equation (Posted on 2013-06-09) Difficulty: 4 of 5
Determine all triplets (a,b,c) of nonzero integers satisfying:
987654321*a + 123456789*b + c = (a + b + c)3

Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Another solution (spoiler) | Comment 2 of 13 |
Charlie's done all the hard work.

Clearly, another solution is (a,b,c) = (-450,-4500,-5050)

We might be able to prove that these are unique by letting 
  a = 450 + X
  b = 4500 + y
  c = 5050 + z
but the math still looks difficult

Or maybe doing something mod 450 would work ...


  Posted by Steve Herman on 2013-06-09 19:46:22
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information