Provide the most elegant proof to the following claim you can produce. Suppose and are nonzero complex numbers and for every positive integer it is true that . then and the are a reordering of the .

Advertisements

Skip to content
# Sum of powers

##
One thought on “Sum of powers”

### Leave a Reply

Provide the most elegant proof to the following claim you can produce. Suppose and are nonzero complex numbers and for every positive integer it is true that . then and the are a reordering of the .

Advertisements

%d bloggers like this:

Given , the assignment defines a complex character of the additive semigroup , which we will denote . The set of such characters is linearly independent, and the hypotheses of the problem imply . This linear combination is then trivial and so the result follows.

LikeLike