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November 23rd, 2016, 11:38 AM   #1
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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?
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November 23rd, 2016, 05:14 PM   #2
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A = b = 2, i = j = 2, c = 4, k = 1
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November 24th, 2016, 09:53 AM   #3
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Quote:
Originally Posted by greg1313 View Post
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?
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November 25th, 2016, 01:57 AM   #4
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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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