number-theory

## 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