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Cube hunting (Posted on 2020-05-29) Difficulty: 3 of 5
Find the set of integers n such that n6 + 24n3 + 192 is a perfect cube.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts I suspect ... | Comment 1 of 8
I think there is no solution.
First a ran a program from n ranging from -10^7 to +10^7 and found no solution.
Then I chose a polynomial:  n^2 + b*n + c and then cubed it, planning to equate the coefficients to those of the polynomial in the problem:
ie 1,0,0,24,0,0,192
But this led only to inconsistencies, so I suspect there is no solution.

I am not sure if I have proved that there is no solution, however.

  Posted by Larry on 2020-05-29 21:42:16
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