Theorems and conjectures for primes: primes in arithmetic progressions, primes of special form, formulas for primes, distribution of primes. Arithmetic functions: number of divisors, sum of divisors, Euler function, Möbius function, Dirichlet convolution, Möbius inversion formula. Mersenne numbers, perfect numbers, Fermat numbers. Polynomial equations modulo n, quadratic residues, Legendre symbol, Jacobi symbol, Kronecker symbol, law of quadratic reciprocity. Pythagorean triples, non-linear Diophantine equations, method of infinite descent, Pell equation. Continued fractions, properties of convergents, best approximation of irrationals by rationals, periodicity of continued fractions. Theorems of Dirichlet and Liouville for diophantine approximations, elements of transcendental number theory. Representations of integers as sums of squares or as sums of higher powers, Waring’s problem. Symmetric and non-symmetric cryptography. Pseudoprimes, Carmichael numbers, deterministic and non-deterministic primality tests. Factorization algorithms.