NUMBER THEORY

Catalog description

Divisibility theory in the integers: greatest common divisor and least common multiple; the division algorithm; the Euclidean algorithm; Diophantine equations. Congruences, special divisibility tests, solving congruence equations, the Chinese remainder theorem. Prime numbers, the infinitude of primes, the Fundamental Theorem of Arithmetic. Number theoretic functions: sigma and tau functions, multiplicative functions, the Euler phi function. Perfect numbers. Fermat and Euler theorems. Applications to cryptography. History of important problems.