31 Jul
2016
31 Jul
'16
5:30 a.m.
It's a nice approach, but I'm missing a step near the end. Why is it true that When n is prime, the *only* integer linear relationships between
the imaginary parts of roots of unity are generated by relationships of the form:
Im[w^k] + Im[w^-k] = 0
? Note that Adam is talking about the *nontrivial* roots of unity. After all, the relation Im[w^0] = 0 has an odd number of terms. But this doesn't mar Adam's argument because w^(a_0 - a_1), ... are all unequal to 1 (which is I suppose what Adam was getting at by saying "Note that none of these terms are zero"). Jim Propp