Number theory

Notes on divisibility, prime numbers, congruences, and the deeper structures behind integer arithmetic. Each piece breaks down a specific theorem, identity, or technique — from Euclidean algorithm fundamentals to modular arithmetic and its applications. The focus is on clear reasoning: why things work, not just how to apply them. A place to build solid intuition for one of mathematics’ oldest and most elegant branches.

The Goldbach-Euler Theorem: Why the Sum of Reciprocals of Perfect Powers Equals 1

How Many Perfect Powers Are There Below 1000? Step-by-Step Count

First of all, thank you to everyone who thought about the problem, worked through the numbers, and shared their answers…

Benford’s Law Explained: Why We Love Round Numbers and What Math Says About It

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