number-theory
Installation
SKILL.md
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