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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    
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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

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