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 Cubic Equation (Posted on 2013-06-09)
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.)
 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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