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Oct 22, 2021 at 1:21 comment added GGT Thanks for pointing it out. At least I can see I have to add one more condition $a_i, c_i $ being rational. And then it might imply that the solution will be algebraic still not rational. If $c_i$ are integers we get the solution is rational.
S Oct 21, 2021 at 21:57 review First answers
Oct 21, 2021 at 22:02
S Oct 21, 2021 at 21:57 history answered Diego Santos CC BY-SA 4.0