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Apr 16, 2022 at 20:08 comment added François Brunault I confirm that your argument works to show the non-vanishing of the sum $S_{N,b}$ in my answer for odd $N$. For clarity I included the argument in my answer.
Apr 16, 2022 at 17:45 comment added François Brunault Thanks! Meanwhile, building on this, I give an argument for general $N$, which I think is ok with your previous argument, and should also be ok with your new argument.
Apr 16, 2022 at 17:26 history edited LSpice CC BY-SA 4.0
Link to @FrançoisBrunault's idea
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