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 re: preli etc: | Comment 4 of 13 |
(In reply to preliminary computer results (spoiler) by Charlie)

Is  there any reason to assume that each of a,b,c is a positive number? 

995<x < 31427  does not imply this.

IMHO  the above statement leads to the conclusion that the range of numbers needed to find ALL solutions by an exhaustive search is infinite thus precluding trying.

A  triplet like a=10^25,  b=55-10^25,  c=1 is within a+b+c definition. So is  a=25000,  b=-1000,  c=1000.

My suggestion: Stay with your program solution, change the puzzle wording: i.e. positive instead of nonzero.

Edited on June 10, 2013, 6:35 am
  Posted by Ady TZIDON on 2013-06-10 01:52:10

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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information