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:
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