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Apr 17, 2022 at 15:52 comment added GH from MO @DenisSerre Good that you accepted François' answer. The main ideas are his. He started the solution, and he finished it. I only contributed an intermediate calculation, which is rather standard.
Apr 17, 2022 at 6:25 vote accept Denis Serre
Apr 17, 2022 at 6:25 comment added Denis Serre @GHfromMO. I hesitated to accept either solution, because both of you contributed significantly to the complete solution of the question. But if you suggest that François' answer be accepted, I'll follow you.
Apr 16, 2022 at 20:06 history edited François Brunault CC BY-SA 4.0
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Apr 16, 2022 at 17:45 comment added GH from MO Thanks for working out the general case. I rewrote my answer several times. I had a version with Galois conjugates, a version with residue calculation, a version where I suspected the generalization for general $N$, a version were I thought I generalized for general $N$, and finally the clean short version for odd $N$. Your ideas are very nice, and your answer should be accepted.
Apr 16, 2022 at 17:41 history answered François Brunault CC BY-SA 4.0