# Number Theory

> Properties of integers

- Skill: `ffsshhttiikk/number-theory` (Agent Skill)
- Install (CLI): `npx skillmds@latest add ffsshhttiikk/number-theory`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ffsshhttiikk/number-theory/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: MIT
- Author: ffsshhttiikk (https://skillmd.com/u/ffsshhttiikk)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/ffsshhttiikk/number-theory

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## What I do
- Apply divisibility and prime factorization
- Solve Diophantine equations
- Work with modular arithmetic and congruences
- Apply Euler's theorem and Fermat's little theorem
- Analyze continued fractions
- Study cryptographic applications

## When to use me
When working with integer problems, cryptography, or coding theory.

## Key Concepts
- **Euclidean Algorithm**: gcd(a,b) = gcd(b, a mod b) for greatest common divisor
- **Prime Factorization**: Unique up to order (Fundamental Theorem of Arithmetic)
- **Modular Arithmetic**: a ≡ b (mod n) means n divides (a-b)
- **Euler's Totient**: φ(n) = count of integers ≤n coprime to n
- **Fermat's Little Theorem**: a^{p-1} ≡ 1 (mod p) for prime p, a not divisible by p
- **Chinese Remainder Theorem**: System of congruences has unique solution mod product