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November 23rd, 2016, 11:38 AM  #1 
Newbie Joined: Sep 2014 From: England Posts: 7 Thanks: 1  Vaguely related to FLT...
It's well known that no integer solution exists for A^3 + B^3 = C^3. But is anything known about (A^3)*(I^2) + (B^3)*(J^2) = (C^3)*(K^2) where I,J,K are also integers? Is there a way of finding solution(s) to an equation of this form? 
November 23rd, 2016, 05:14 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond 
A = b = 2, i = j = 2, c = 4, k = 1

November 24th, 2016, 09:53 AM  #3 
Newbie Joined: Sep 2014 From: England Posts: 7 Thanks: 1  
November 25th, 2016, 01:57 AM  #4 
Banned Camp Joined: Dec 2012 Posts: 1,028 Thanks: 24 
To have an answer you've to fix ALL the relations between your terms. One possible case is if you can arrive to a multiple of: $ 1^3 = 3^22^3 $ Last edited by complicatemodulus; November 25th, 2016 at 02:00 AM. 

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