To move ahead on the Kummer Class Formula, it is necessary to delve into Dirichlet Characters and L-Functions. Properly appreciating these ideas requires a solid understanding of cyclic groups.
I think that it makes sense at this point to take a break from Kummer's Class Formula and trace the development of group theory from the quadratic equation to Galois's famous proof.
Once I have gone into more detail about group theory and in particular, cyclic groups, I will resume the development of Kummer's Class Formula.
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