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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 Thanks from topsquark and William the Conker
November 24th, 2016, 09:53 AM   #3
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Quote:
 Originally Posted by greg1313 A = b = 2, i = j = 2, c = 4, k = 1
Thank you!

Although I should have been more precise (after all, this is a maths forum).

I should have added that all integers are >=2, and that AI,BJ and CK are pairwise coprime.

Any suggestions?

 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: $1^3 = 3^2-2^3$ Last edited by complicatemodulus; November 25th, 2016 at 02:00 AM.

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