Number Theory

The study of properties and relationships of integers, especially prime numbers.

• fundamental theorem of arithmetic:: every integer greater than 1 is a unique product of primes
• modular arithmetic studies remainders and congruences, forming the basis of cryptography
• Riemann hypothesis:: the deepest open conjecture about prime distribution
• Euler’s totient function counts integers coprime to n, central to RSA
• Diophantine equations seek integer solutions to polynomial equations
• Fermat’s last theorem:: proved by Andrew Wiles in 1995 using elliptic curves
• Foundation of cryptography, hash functions, and zero-knowledge proofs
• Related: algebra, set theory, combinatorics, logic, game theory