Topics in p-Adic Concepts and Techniques
Numbered in the order to learn them.
p-Adic Absolute Value
Hensel's Lemma
Lifting the Exponent (LTE)
What Are the p-Adic Numbers?
What Are Continuous p-Adic Functions?
Discrete Calculus and Mahler's Theorem
Comparing the Real and p-Adic Absolute Values
Ostrowski's Theorem
Freshman's Dream (Frobenius): Expanding pth Powers Modulo p
Generating Functions and Lucas' Theorem
p-Adic Valuation of a Factorial (Legendre's Formula)
p-Adic Valuation of a Binomial Coefficient (Kummer's Theorem)
Proofs of Bertrand's Postulate
Combinatorial Proof of Lucas' Theorem
Exponentials and Skolem's p-Adic Method
Skolem-Mahler-Lech Theorem on Linear Recurrences