P-adic Expansion: Unique Representations and Power Series

This lecture covers the topic of p-adic expansion, focusing on the unique representations and power series. The instructor discusses the space of C.S., emphasizing the discovery of a unique representative in Zp. Various ways to think about this representative are explored, such as explicit C.S. and power series. The lecture demonstrates how these representations are related and how they can be used to compute p-adic expansions. The discussion progresses through examples and comparisons, highlighting the homomorphism from Zp to Z/p^mZ. The lecture concludes by showcasing the practical application of these concepts in computing p-adic expansions.