Hi everyone!
Today I'd like to write a bit on the amazing things you can get out of a power series by putting roots of unity into its arguments. It will be another short story without any particular application in competitive programming (at least I don't know of them yet, but there could be). But I find the facts below amazing, hence I wanted to share them.
You're expected to know some basic stuff about the discrete Fourier transform and a bit of linear algebra to understand the article.