Reciprocals, powers of 10, and Euler's totient function II | Data Structures Math Foundations 203

We introduce the idea of the unit group U(n) of a natural number n. This is an algebraic object that contains important data about how multiplication mod n works, even for a composite number n. There is a natural connection with Euler's totient function, and we will see how to exploit this to figure out how big the repeated cycles are for a fraction such as 1/n, even for a big number n.

Along the way, we will summarize some important number theory / group theory facts relating to the unit groups, including prominently Lagrange's theorem.

You might notice the video looks a bit different--I now have a new camera, and am working on getting my head around using it!

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