Mathematical induction, divisibility, prime numbers, Euclidean algorithm, factorization methods, Diophantine equations, congruences, Chinese remainder theorem, systems of congruences, Fermat?s little theorem, multiplicative functions, public key cryptography, primitive roots, primality tests, quadratic reciprocity, Pythagorean triples, Fermat?s last theorem, and sums of squares. Other topics may include continued fractions and partitions.